Updated on 2021/06/22

写真b

 
JIMBO Michio
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Field of Study: Mathematics
Graduate School of Science Field of Study: Mathematics
Title*
Specially Appointed Professor
Degree
理学修士 ( 京都大学 ) / 理学博士 ( 京都大学 ) / Master ( Kyoto University )
Contact information
Mail Address
Research Theme*
  • 統計物理学や場の理論に現れる厳密に解ける模型の数理に興味をもち、代数的なアプローチで研究を進めている。最近は特に格子模型の相関関数を重点的に研究しているが、関連して現れるリー代数や量子群などの代数構造、共形場理論における指標公式のような組合せ的側面にも興味がある。

  • Research Interests
  • quantum integrable systems

  • Campus Career*
    • 4 2017 - Present 
      College of Science   Department of Mathematics   Specially Appointed Professor
    • 4 2017 - Present 
      Graduate School of Science   Field of Study: Mathematics   Specially Appointed Professor
    • 4 2017 - Present 
      Graduate School of Science   Field of Study: Mathematics   Specially Appointed Professor
    • 4 2009 - 3 2017 
      College of Science   Department of Mathematics   Professor
     

    Research Areas

    • Natural Science / Basic analysis

    • Natural Science / Mathematical analysis

    Research History

    • 4 2017 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Specially Appointed Professor

      More details

    • 4 2017 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Specially Appointed Professor

      More details

    • 4 2017 - Present 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Specially Appointed Professor

      More details

    • 6 2012 - Present 
      The University of Tokyo

      More details

    • 4 2010 - Present 
      Kyoto University   Professor Emeritus

      More details

    • 4 2009 - 3 2017 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Professor

      More details

    • 4 2000 - 3 2009 
      The University of Tokyo   Graduate School of Mathematical Sciences

      More details

    • 4 1992 - 3 2000 
      Kyoto University   Graduate School of Science

      More details

    • 11 1988 - 3 1992 
      Kyoto University   Faculty of Science

      More details

    • 4 1976 - 10 1988 
      Kyoto University   Research Institute for Mathematical Sciences

      More details

    ▼display all

    Education

    • - 3 1976 
      Kyoto University   Graduate School, Division of Natural Science

      More details

      Country: Japan

      researchmap

    • - 3 1976 
      Kyoto University   Graduate School, Division of Natural Science

      More details

      Country: Japan

      researchmap

    • - 3 1974 
      The University of Tokyo   Faculty of Science

      More details

      Country: Japan

      researchmap

    Awards

    • 3 2013  
      Dannie Heineman Prize 
       
      Michio Jimbo, Tetsuji Miwa

      More details

      Award type:International academic award (Japan or overseas)  Country:United States

      researchmap

    • 7 2010  
      Wigner Medal 
       
      Michio Jimbo

      More details

      Award type:International academic award (Japan or overseas)  Country:United Kingdom

      researchmap

    • 1 2000  
      朝日文化財団  朝日賞 
       
      三輪哲二, 神保道夫

      More details

      Award type:Award from publisher, newspaper, foundation, etc.  Country:Japan

      researchmap

    • 6 1993  
      日本学士院  日本学士院賞 
       
      神保道夫

      More details

      Award type:Other  Country:Japan

      researchmap

    • 10 1987  
      日本数学会  日本数学会秋期賞 
       
      三輪哲二, 神保道夫

      More details

      Award type:Award from Japanese society, conference, symposium, etc.  Country:Japan

      researchmap

    Papers

    • Finite Type Modules and Bethe Ansatz for Quantum Toroidal gl(1) Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      COMMUNICATIONS IN MATHEMATICAL PHYSICS356 ( 1 ) 285 - 327   11 2017

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

      We study highest weight representations of the Borel subalgebra of the quantum toroidal algebra with finite-dimensional weight spaces. In particular, we develop the q-character theory for such modules. We introduce and study the subcategory of 'finite type' modules. By definition, a module over the Borel subalgebra is finite type if the Cartan like current has a finite number of eigenvalues, even though the module itself can be infinite dimensional. We use our results to diagonalize the transfer matrix T (V,W) (u; p) analogous to those of the six vertex model. In our setting T (V,W) (u; p) acts in a tensor product W of Fock spaces and V is a highest weight module over the Borel subalgebra of quantum toroidal with finite-dimensional weight spaces. Namely we show that for a special choice of finite type modules V the corresponding transfer matrices, Q(u; p) and , are polynomials in u and satisfy a two-term TQ relation. We use this relation to prove the Bethe Ansatz equation for the zeroes of the eigenvalues of Q(u; p). Then we show that the eigenvalues of T (V,W) (u; p) are given by an appropriate substitution of eigenvalues of Q(u; p) into the q-character of V.

      DOI: 10.1007/s00220-017-2984-9

      researchmap

    • Integrals of motion from quantum toroidal algebras Peer-reviewed

      B. Feigin, M. Jimbo, E. Mukhin

      JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL50 ( 46 )   11 2017

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:IOP PUBLISHING LTD  

      We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors.
      That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model.
      We also discuss the (gl(m), gl(n)) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine sl(2).

      DOI: 10.1088/1751-8121/aa8e92

      researchmap

    • Branching rules for quantum toroidal gl(n) Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      ADVANCES IN MATHEMATICS300   229 - 274   9 2016

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

      We construct an analog of the subalgebra Ugl(n) circle times Ugl(m) subset of Ugl(m + n) in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra. (C) 2016 Elsevier Inc. All rights reserved.

      DOI: 10.1016/j.aim.2016.03.019

      researchmap

    • Quantum toroidal gl(1) and Bethe ansatz Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL48 ( 24 )   6 2015

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:IOP PUBLISHING LTD  

      We establish the method of Bethe ansatz for the XXZ type model obtained from the R matrix associated to quantum toroidal gl(1). We do this by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.

      DOI: 10.1088/1751-8113/48/24/244001

      researchmap

    • Representations of quantum toroidal gln Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      Journal of Algebra380   78 - 108   2013

      More details

    • Quantum toroidal gl1-algebra: Plane partitions Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      Kyoto Journal of Mathematics52 ( 3 ) 621 - 659   2012

      More details

      Language:English  

      DOI: 10.1215/21562261-1625217

      researchmap

    • Fermionic structure in the sine-Gordon model: Form factors and null-vectors Peer-reviewed

      M. Jimbo, T. Miwa, F. Smirnov

      Nuclear Physics B852 ( 2 ) 390 - 440   2011

      More details

    • Hidden Grassmann Structure in the XXZ Model V: Sine-Gordon Model Peer-reviewed

      M. Jimbo, T. Miwa, F. Smirnov

      Letters in Mathematical Physics96 ( 1-3 ) 325 - 365   2011

      More details

      Language:English  

      DOI: 10.1007/s11005-010-0438-9

      researchmap

    • Hidden Grassmann Structure in the XXZ Model IV: CFT Limit Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov

      Communications in Mathematical Physics299 ( 3 ) 825 - 866   2010

      More details

      Language:English  

      DOI: 10.1007/s00220-010-1051-6

      researchmap

    • Hidden Grassmann structure in the XXZ model III Peer-reviewed

      M.jimbo,T.Miwa, F.Smirnov

      Journal of Physics A42   304018   30 6 2009

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Hidden Grassmann structure in the XXZ model II Peer-reviewed

      H.Boos, M.Jimbo, T.Miwa.F.Smirnov, Y.Takeyama

      Communications in Mathematical Physics286   875 - 932   30 4 2009

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Completeness of a fermionic basis in the homogeneous XXZ model Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov

      Journal of Mathematical Physics50 ( 9 )   2009

      More details

      Language:English  

      DOI: 10.1063/1.3147206

      researchmap

    • Hidden Grassmann structure in the XXZ model Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama

      Commun.Math.Phys.272 ( 1 ) 263 - 281   2007

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      For the critical XXZ model, we consider the space W of operators which are<br />
      products of local operators with a disorder operator. We introduce two<br />
      anti-commutative family of operators b(z), c(z) which act on the space W. These<br />
      operators are constructed as traces over representations of the q-oscillator<br />
      algebra, in close analogy with Baxter&#039;s Q-operators. We show that the vacuum<br />
      expectation values of operators in W can be expressed in terms of an<br />
      exponential of a quadratic form of b(z), c(z).

      DOI: 10.1007/s00220-007-0202-x

      researchmap

    • Reduced qKZ equation and correlation functions of the XXZ model

      H.Boos, M.Jimbo, T.Miwa, F.Smirnov, Y.Takeyama

      Communications in Mathematical Physics261   245 - 276   31 12 2006

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A recursion formula for the correlation functions of an inhomogeneous XXX model Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama

      St. Petersburg Math. J.17 ( 1 ) 85 - 117   2006

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      A new recursion formula is presented for the correlation functions of the<br />
      integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators<br />
      involving n consecutive lattice sites to those with n-1 and n-2 sites. In a<br />
      series of papers by V. Korepin and two of the present authors, it was<br />
      discovered that the correlators have a certain specific structure as functions<br />
      of the inhomogeneity parameters. Our formula allows for a direct proof of this<br />
      structure, as well as an exact description of the rational functions which has<br />
      been left undetermined in the previous works.

      researchmap

    • Algebraic representation of correlation functions in integrable spin chains Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama

      ANNALES HENRI POINCARE7 ( 7-8 ) 1395 - 1428   2006

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:BIRKHAUSER VERLAG AG  

      Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.

      DOI: 10.1007/s00023-006-0285-5

      researchmap

    • Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama

      Lett.Math.Phys.75 ( 3 ) 201 - 208   2006

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      We consider a finite sub-chain on an interval of the infinite XXX model in<br />
      the ground state. The density matrix for such a subsystem was described in our<br />
      previous works for the model with inhomogeneous spectral parameters. In the<br />
      present paper, we give a compact formula for the physically interesting case of<br />
      the homogeneous model.

      DOI: 10.1007/s11005-006-0054-x

      researchmap

    • Traces on the Sklyanin algebra and correlation functions of the eight-vertex model Peer-reviewed

      H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama

      J.Phys. A38 ( 35 ) 7629 - 7660   2005

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      We propose a conjectural formula for correlation functions of the Z-invariant<br />
      (inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It<br />
      states that correlation functions are linear combinations of products of three<br />
      transcendental functions, with theta functions and derivatives as coefficients.<br />
      The transcendental functions are essentially logarithmic derivatives of the<br />
      partition function per site. The coefficients are given in terms of a linear<br />
      functional on the Sklyanin algebra, which interpolates the usual trace on<br />
      finite dimensional representations. We establish the ex...

      DOI: 10.1088/0305-4470/38/35/003

      researchmap

    • A functional model for the tensor product of level q highest and level -1 lowest modules for the quantum affine algebra Uq(\tilde{sl}2) Peer-reviewed

      B.Feigin, M.Jimbo, T.Miwa, E.Mukhin, Y.Takeyama

      European Journal of Combinatorics25   1197 - 1229   31 12 2004

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Counting minimal form factors of the restricted sine-Gordon model Peer-reviewed

      M.jimbo,T.Miwa, Y.Takeyama

      Moscow Journal of Mathematics4   777 - 836   31 12 2004

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Spaces of coinvariants and fusion product I Peer-reviewed

      B.Feigin, M.jimbo, R.Kedem, S.Loktev, T.Miwa

      Duke Mathematical Journal125   549 - 588   31 12 2004

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Symmetric polynomials vanishing on the diagonals shifted by roots of unity Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin, Y. Takeyama

      Int. Math. Res. Not.2003 ( 18 ) 999 - 1014   2003

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      For a pair of positive integers (k,r) with r&gt;1 such that k+1 and r-1 are<br />
      relatively prime, we describe the space of symmetric polynomials in variables<br />
      x_1,...,x_n which vanish at all diagonals of codimension k of the form<br />
      x_i=tq^{s_i}x_{i-1}, i=2,...,k+1, where t and q are primitive roots of unity of<br />
      orders k+1 and r-1.

      researchmap

    • Vertex operator algebra arising from the minimal series M(3,p) Peer-reviewed

      B.Feigin, M.jimbo, T.Miwa

      Proceedings of Math Phys Odessey 2001   31 12 2002

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A differential ideal of symmetric polynomials spanned by Jack polynomials at β = -(r - 1)/(k + 1) Peer-reviewed

      B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

      International Mathematics Research Notices ( 23 ) 1223 - 1237   2002

      More details

      Language:English  

      researchmap

    • Free field construction of the ABF models in regime II Peer-reviewed

      M.Jimbo, H.Konno, S.Odake, Y.Pugai, J.Shiraishi

      Journal of Statistical Physics102   883 - 921   31 12 2001

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Elliptic algebra Uqp(\hat{sl}2) Peer-reviewed

      M.Jimbo, H.Konno, S.Odake, J.Shiraishi

      Communications in Mathematical Physics199   605 - 647   31 12 1999

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Quasi-Hopf twistors for elliptic quantum groups

      M.Jimboet

      Tranformation groups4   303-327   4 1999

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Elliptic algebra U-q,U-p((sl)over-cap(2)): Drinfeld currents and vertex operators Peer-reviewed

      M Jimbo, H Konno, S Odake, J Shiraishi

      COMMUNICATIONS IN MATHEMATICAL PHYSICS199 ( 3 ) 605 - 647   1 1999

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

      We investigate the structure of the elliptic algebra U-q,U-p((sl)over-cap(2)) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra U-q((sl)over-cap(2)), which are elliptic analogs of the Drinfeld currents. They enable us to identify U-q,U-p((sl)over-cap(2)) with the tensor product of U-q((sl)over-cap(2)) and a Heisenberg algebra generated by P, Q with [Q, P] = 1. In terms of these currents, we construct an L operator satisfying the dynamical RLL relation in the presence of the central element c. The vertex operators of Lukyanov and Pugai arise as "intertwiners" of U-q,U-p((sl)over-cap(2)) for the level one representation, in the sense to be elaborated on in the text. We also present vertex operators with higher level/spin in the free field representation.

      researchmap

    • Quasi-Hopf twistors for elliptic quantum groups Peer-reviewed

      M Jimbo, H Konno, S Odake, J Shiraishi

      TRANSFORMATION GROUPS4 ( 4 ) 303 - 327   1999

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:BIRKHAUSER BOSTON INC  

      The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al. [FIJKMY1], Felder [Fe]). Fr phi nsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U-q(g) In this paper we present an explicit formula for the twisters in the form of an infinite product of the universal R matrix of U-q,(S). We also prove the shifted cocycle condition for the twisters, thereby completing Fr phi nsdal's findings.
      This construction entails that, for generic values of the deformation parameters, the representation theory for U-q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A(q,p)(sl(2)).

      researchmap

    • Algebra of screening operators and the deformed Wn algebra Peer-reviewed

      B.Feigin, M.Jimbo, T.Miwa, A.Odesski, Ya.Pugai

      Communications in Mathematical Physics191   501 - 541   31 12 1998

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Massless XXZ model and degeneration of the elliptic algebra A(q,p)((s)over-cap-l(2)) Peer-reviewed

      M Jimbo, H Konno, T Miwa

      DEFORMATION THEORY AND SYMPLECTIC GEOMETRY20   117 - 138   1997

      More details

      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER  

      Following Lukyanov's bosonization formula for the sine-Gordon model, we present the bosonization of the massless XXZ model by using the free boson on tile real line. We discuss its connection to the degeneration of tile elliptic algebra A(q,p)(&lt;(sl)over cap&gt;(2)).

      researchmap

    • Bosonization of vertex operators for the A(1)n-1 face models

      Y.Asai, M.Jimbo, T.Miwa, Ya.Pugai

      Journal of Physics A29   6595 - 6616   31 12 1996

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Quantum Knizhnik-Zamolodchikov equation at |q|=1 and correlation functions of the XXZ model in the gapless regime Peer-reviewed

      M.Jimbo, T.Miwa

      Journal of Physics A29   2923 - 2958   31 12 1996

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A q-Analog of the Sixth Painlevé Equation

      Michio Jimbo, Hidetaka Sakai

      Letters in Mathematical Physics38 ( 2 ) 145 - 154   1996

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Netherlands  

      A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy-preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.

      DOI: 10.1007/BF00398316

      Scopus

      researchmap

    • XXZ chain with a boundary Peer-reviewed

      M.jimbo,R.Kedem, T.Kojima, H.Konno, T.Miwa

      Nuclear Physics B441   437 - 470   31 12 1995

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials Peer-reviewed

      M. Jimbo, R. Kedem, H. Konno, T. Miwa, J. U H Petersen

      Journal of Physics A: Mathematical and General28 ( 19 ) 5589 - 5606   1995

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      The level-1 integrable highest weight modules of Uq(sl 2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-1 module generated by components of vertex operators. Each level-1 module is a direct sum of finite-dimensional irreducible level-0 modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-1 modules.

      DOI: 10.1088/0305-4470/28/19/014

      Scopus

      researchmap

    • An elliptic quantum algebra for A#Dpq(sl#D2)

      O.Foda e

      Lett. Math. Phys. 32,   259-268   4 1994

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Smirnov's integrals and quantum Knizhnik-Zamolodchikov equation of level O

      M.Jimbo

      J. Phys. A27   3267-3283   4 1994

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Vertex operators in solvable lattice models Peer-reviewed

      O.Foda e

      J. Math. Phys.35,13-46   4 1994

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Diagonalization of the XXZ Hamiltonian by vertex operators Peer-reviewed

      B.Davies, O.Foda, M.jimbo, T.Miwa, A.Nakayashiki

      Communications in Mathematical Physics151   89 - 153   31 12 1993

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Difference equations for the correlation functions of the eight-vertex model Peer-reviewed

      M. Jimbo, T. Miwa, A. Nakayashiki

      Journal of Physics A: Mathematical and General26 ( 9 ) 2199 - 2209   7 5 1993

      More details

      Language:English  

      DOI: 10.1088/0305-4470/26/9/015

      researchmap

    • Correlation functions of the XXZ model for \Delta<-1 Peer-reviewed

      M.Jimbo, T.Miwa, K.Miki, A.Nakayashiki

      Physics Letters A168   256 - 263   31 12 1992

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Crystal base and q-vertex operators Peer-reviewed

      E.Date,M.Jimbo, M.Okado

      Communications in Mathematical Physics155   47 - 69   31 12 1991

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • COMBINATORICS OF REPRESENTATIONS OF UQ[SL(N)] AT Q = 0 Peer-reviewed

      M JIMBO, KC MISRA, T MIWA, M OKADO

      COMMUNICATIONS IN MATHEMATICAL PHYSICS136 ( 3 ) 543 - 566   1991

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

      The q = 0 combinatorics for U(q)(sI(n)) is studied in connection with solvable lattice models. Crystal bases of highest weight representations of U(q)(sI(n)) are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors at q = 0. It is shown that the crystal graphs for finite tensor products of l-th symmetric tensor representations of U(q)(sI(n)) approximate the crystal graphs of level l representations of U(q)(sI(n)). The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for U(q)(sI(n)).

      researchmap

    • GENERALIZED CHIRAL POTTS MODELS AND MINIMAL CYCLIC REPRESENTATIONS OF UQ(GL(N,C)) Peer-reviewed

      E DATE, M JIMBO, K MIKI, T MIWA

      COMMUNICATIONS IN MATHEMATICAL PHYSICS137 ( 1 ) 133 - 147   1991

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

      We present for odd N a construction of the N(n-1)-state generalization of the chiral Potts model proposed recently by Bazhanov et al. The Yang-Baxter equation is proved.

      researchmap

    • Representations of Uq(gl(n,C)) at q=0 and the Robinson-Schensted correspondence Invited Peer-reviewed

      E.Date, M.Jimbo, T.Miwa

      Physics and Mathematics of Strings   31 12 1990

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • HYPERGEOMETRIC TYPE INTEGRALS AND THE SL(2,C) KNIZHNIK-ZAMOLODCHIKOV EQUATION Peer-reviewed

      E DATE, M JIMBO, A MATSUO, T MIWA

      INTERNATIONAL JOURNAL OF MODERN PHYSICS B, VOL 4, NO 5, APRIL 19904   1049 - 1057   1990

      More details

      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

      researchmap

    • Paths, Maya diagrams and representations of \hat{sl}(r,C)

      E.Date, M.jimbo, A.Kuniba, T.Miwa, M.Okado

      Advanced Studies in Pure Mathematics19   149 - 191   31 12 1989

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • PATHS, MAYA DIAGRAMS AND REPRESENTATIONS OF SL(R, C) Peer-reviewed

      E DATE, M JIMBO, A KUNIBA, T MIWA, M OKADO

      COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE308 ( 5 ) 129 - 132   2 1989

      More details

      Language:French   Publishing type:Research paper (scientific journal)   Publisher:GAUTHIER-VILLARS  

      researchmap

    • One-dimensional configuration sums in vertex models and affine Lie algebra characters Peer-reviewed

      E. Date, M. Jimbo, A. Kuniba, T. Miwa, M. Okado

      Letters in Mathematical Physics17 ( 1 ) 69 - 77   1989

      More details

      Language:English  

      DOI: 10.1007/BF00420017

      researchmap

    • Exactly solvable SOS models II

      E.Date,M.Jimbo, A.Kuniba, T.Miwa, M.Okado

      Advanced Studies in Pure Matehmatics16   17 - 122   31 12 1988

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • SOLVABLE LATTICE MODELS RELATED TO THE VECTOR REPRESENTATION OF CLASSICAL SIMPLE LIE-ALGEBRAS Peer-reviewed

      M JIMBO, T MIWA, M OKADO

      COMMUNICATIONS IN MATHEMATICAL PHYSICS116 ( 3 ) 507 - 525   1988

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

      researchmap

    • Exactly solvable SOS models Peer-reviewed

      E.Date, M.jimbo, A.Kuniba, T.Miwa, M.Okado

      Nuclear Physics B290   231 - 273   31 12 1987

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A q-analogue of U(gl(N+1)), Hecke algebra and the Yang-Baxter equation Peer-reviewed

      M.Jimbo

      Letters in Mathematical Physics11   247 - 252   31 12 1986

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Fusion of the eight-vertex SOS model Peer-reviewed

      E.Date, M.jimbo, T.Miwa, M.Okado

      Letters in Mathematical Physics12   209 - 215   31 12 1986

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Solvable lattice models with broken ZN symmetry and Hecke's indefinite modular forms

      M.Jimbo, T.Miwa, M.Okado

      Nuclear Physics B275   517 - 545   31 12 1986

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • QUANTUM R-MATRIX FOR THE GENERALIZED TODA SYSTEM

      M JIMBO

      COMMUNICATIONS IN MATHEMATICAL PHYSICS102 ( 4 ) 537 - 547   1986

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

      researchmap

    • A q-difference analogue of U(g) and the Yang-Baxter equation Peer-reviewed

      M.Jimbo

      Letters in Mathematical Physics10   63 - 69   31 12 1985

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A q-difference analogue of U(g) and the Yang-Baxter equation

      Letters in Mathematical Physics10   4 1985

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • A SOLVABLE LATTICE MODEL AND RELATED ROGERS-RAMANUJAN TYPE IDENTITIES Peer-reviewed

      M JIMBO, T MIWA

      PHYSICA D15 ( 3 ) 335 - 353   1985

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

      researchmap

    • Solitons and infinite dimensional Lie algebras Peer-reviewed

      M.Jimbo, T.Miwa

      Publ.RIMS,Kyoto Univ.19   943 - 1001   31 12 1983

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Landau-Lifshitz equation: Solitons, quasi-periodic solutions and infinite-dimensional Lie algebras Peer-reviewed

      E. Date, M. Jimbo, M. Kashiwara, T. Miwa

      Journal of Physics A: Mathematical and General16 ( 2 ) 221 - 236   1983

      More details

      Language:English  

      DOI: 10.1088/0305-4470/16/2/006

      researchmap

    • Monodromy problem and the boundary condition for some Painleve equations Peer-reviewed

      M.Jimbo

      Publ.RIMS, Kyoto Univ.18   1137 - 1161   31 12 1982

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Transformation groups for soliton equations

      E.Date, M.jimbo, M.Kashiwara, T.Miwa

      Publ.RIMS, Kyoto Univ.18   1077 - 1110   31 12 1982

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Transformation groups for soliton equations

      E.Date, M.jimbo, M.Kashiwara, T.Miwa

      Publ.RIMS, Kyoto Univ.18   1077 - 1110   31 12 1982

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Transformation groups for soliton equations

      Publication RIMS, Kyoto University18   4 1982

      More details

      Language:English   Publishing type:Research paper (bulletin of university, research institution)  

      researchmap

    • Transformation groups for soliton equations. IV. A new hierarchy of soliton equations of KP-type Peer-reviewed

      E. Date, M. Jimbo, M. Kashiwara, T. Miwa

      Physica D: Nonlinear Phenomena4 ( 3 ) 343 - 365   1982

      More details

    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients III

      M.Jimbo, T.Miwa

      Physica D4   26 - 46   31 12 1981

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Transformation groups for soliton equations III

      E.Date,M.Jimbo, M.Kashiwara, T.Miwa

      J.Phys.Soc.Jpn50   3806 - 3812   31 12 1981

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • 1/C EXPANSION OF THE DENSITY-MATRIX FOR THE DELTA-FUNCTION BOSE-GAS Peer-reviewed

      M JIMBO, T MIWA

      PHYSICAL REVIEW D24 ( 12 ) 3169 - 3173   1981

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMERICAN PHYSICAL SOC  

      researchmap

    • KP HIERARCHIES OF ORTHOGONAL AND SYMPLECTIC TYPE - TRANSFORMATION GROUPS FOR SOLITON-EQUATIONS .6. Peer-reviewed

      E DATE, M JIMBO, M KASHIWARA, T MIWA

      JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN50 ( 11 ) 3813 - 3818   1981

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:PHYSICAL SOCIETY JAPAN  

      researchmap

    • MONODROMY PRESERVING DEFORMATION OF RAMIFIED SOLUTIONS TO (DELTA-M2)U=O Peer-reviewed

      M JIMBO, M KASHIWARA, T MIWA

      JOURNAL OF MATHEMATICAL PHYSICS22 ( 11 ) 2581 - 2587   1981

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER INST PHYSICS  

      researchmap

    • Density matrix of an impenetrable Bose gas and the fifth Painleve transcendent Peer-reviewed

      M.Sato, T.Miwa, M.Jimbo, Y.Mori

      Physica D1   80 - 158   31 12 1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Holonomic Quantum Fields V Peer-reviewed

      M.Sato, T.Miwa, M.Jimbo

      Publ.RIMS, Kyoto Univ.16   531 - 584   31 12 1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients I Peer-reviewed

      M.Jimbo, T.Miwa, K.Ueno

      Physica D2   306 - 352   31 12 1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Monodromy preserving deformation of linear ordinary differential equations with rational coefficients II

      M.Jimbo, T.Miwa

      Physica D2   407 - 448   31 12 1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • DEFORMATION OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS .1. Peer-reviewed

      M JIMBO, T MIWA

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES56 ( 4 ) 143 - 148   1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      researchmap

    • DEFORMATION OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS .2. Peer-reviewed

      M JIMBO, T MIWA

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES56 ( 4 ) 149 - 153   1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      researchmap

    • DEFORMATION OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS .3. Peer-reviewed

      M JIMBO, T MIWA

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES56 ( 6 ) 269 - 274   1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      researchmap

    • STUDIES ON HOLONOMIC QUANTUM FIELDS .17. Peer-reviewed

      M JIMBO, T MIWA

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES56 ( 9 ) 405 - 410   1980

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      researchmap

    • Holonomic Quantum Fields II Peer-reviewed

      M.Sato, T.Miwa, M.Jimbo

      Oubl.RIMS, Kyoto Univ.15   201 - 278   31 12 1979

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Holonomic Quantum Fields III Peer-reviewed

      M.Sato, T.Miwa, M.Jimbo

      Publ.RIMS, Kyoto Univ.15   577 - 629   31 12 1979

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Holonomic Quantum Fields IV Peer-reviewed

      M.Sato, T.Miwa, M.Jimbo

      Publ. RIMS, Kyoto Univ.15   871 - 972   31 12 1979

      More details

      Language:English   Publishing type:Research paper (scientific journal)  

      researchmap

    • Holonomic quantum fields II-IV

      Publication RIMS, Kyoto University15   4 1979

      More details

      Language:English   Publishing type:Research paper (bulletin of university, research institution)  

      researchmap

    • Holonomic Quantum Fields I

      M. Sato, T.Miwa, M.Jimbo

      Publ. RIMS, Kyoto Univ.14   223 - 267   31 12 1978

      More details

      Language:English   Publishing type:Research paper (international conference proceedings)  

      researchmap

    ▼display all

    Misc.

    • An algebraic representation for correlation functions in integrable spin chains

      M.Jimbo

      Algebraic analysis of differential equations   12 2008

      More details

      Language:English   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:Springer  

      researchmap

    • Introduction to Holonomic Quantum Fields for Mathematicians

      Michio Jimbo

      Proceedings of Symposia in Pure Mathematics49   379 - 390   12 1989

      More details

      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:American Mathematical Society  

      researchmap

    • Introduction to Yang-Baxter equation

      Michio Jimbo

      Braid groups, knot theory and statistical mechanics   12 1989

      More details

      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (other)   Publisher:World Scientific Publishing Co.  

      researchmap

    • 2次元の可解な格子模型とモジュラー関数

      神保道夫, 三輪哲二, 尾角正人

      数学40 ( 1 ) 1 - 18   4 1988

      More details

      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)   Publisher:岩波書店  

      researchmap

    • ソリトン方程式と Kac-Moody リー環

      伊達悦朗, 神保道夫, 柏原正樹, 三輪哲二

      数学34 ( 1 ) 1 - 16   4 1982

      More details

      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)   Publisher:岩波書店  

      researchmap

    • タウ関数の理論

      三輪哲二, 神保道夫

      数学32 ( 4 ) 289 - 307   12 1980

      More details

      Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)   Publisher:岩波書店  

      researchmap

    ▼display all

    Books and Other Publications

    • 数学入門辞典

      青本和彦他( Role: Joint editor)

      岩波書店  28 9 2005 

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    • 熱・波動と微分方程式

      俣野博, 神保道夫( Role: Joint author)

      岩波書店  5 3 2004  ( ISBN:4000068768

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    • 複素関数入門

      神保道夫( Role: Sole author)

      岩波書店  12 12 2003  ( ISBN:4000068741

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    • ホロノミック量子場

      神保道夫( Role: Sole author)

      岩波書店  21 12 1998  ( ISBN:4000106546

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    • Algebraic Analysis of Solvable Lattice Models

      Michio Jimbo, Tetsuji Miwa( Role: Edit)

      American Mathematical Society  12 1995  ( ISBN:0821803204

      More details

      Language:English Book type:Scholarly book

      researchmap

    • Solitons

      8 6 1993  ( ISBN:4000108085

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    • 量子群とヤン・バクスター方程式

      神保道夫( Role: Sole author)

      シュプリンガー東京  20 12 1990  ( ISBN:4431705945

      More details

      Language:Japanese Book type:Scholarly book

      researchmap

    ▼display all

    Presentations

    • Representations of quantum toroidal algebras International conference

      Michio Jimbo

      Recent Advances in Quantum Integrable Systems  11 9 2012 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Angers, France  

      researchmap

    • Fermionic basis of local operators in quantum integrable models International conference

      Michio Jimbo

      国際数理物理学会  6 8 2012  International Association of Mathematical Physics

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Aalborg, Denmark  

      researchmap

    • Fermions acting on local operators in the XXZ model: a review International conference

      神保道夫

      対称性、可積分系と表現論  13 12 2011 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Universite Lyon I  

      researchmap

    • Fermionic basis of local operators in the sine-Gordon model International conference

      神保道夫

      第8回ボローニャ共形場理論と可積分模型研究会  9 9 2011 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      researchmap

    • Fermionic basis of local fields in the sine-Gordon model International conference

      神保道夫

      ゲージ・弦理論における可積分性(IGST2011)  15 8 2011 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Perimeter Institute  

      researchmap

    • Fermionic structure in integrable models: from lattice to CFT and massive field theory:II International conference

      神保道夫

      無限解析11--可積分系の最先端---  25 7 2011 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:東京大学数理科学研究科  

      researchmap

    • Fermionic structure in the sine-Gordon model---Recent Developments International conference

      神保道夫

      量子可積分性とゲージ理論  28 3 2011 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Hamilton Mathematical Institute  

      researchmap

    • What are the `full symmetries' in quantum integrable models? International conference

      Michio Jimbo

      物理学における群論的方法  26 7 2010 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Newcastle, UK  

      researchmap

    • One point functions in the sine-Gordon model International conference

      Michio Jimbo

      Recent Advances in Quantum Integrable Systems 10  15 6 2010 

      More details

      Language:English   Presentation type:Oral presentation (invited, special)  

      Venue:LAPTH, Annecy (France)  

      researchmap

    ▼display all

    Professional Memberships

    Research Projects

    • 量子トロイダル代数の可積分系への応用

      日本学術振興会  科学研究費助成事業 

      神保道夫

      More details

      4 2016 - Present

      Authorship:Principal investigator  Grant type:Competitive

      従来の量子可積分系においては1変数ループ代数の量子化である量子アフィン代数が基本的な役割を果たしている。2変数ループ代数の量子化は量子トロイダル代数とよばれる。 量子トロイダル代数を対称性とする量子可積分系はこれまであまり研究されていなかったが、本研究はそれに焦点をあてる。

      researchmap

    • Algebraic structure of integrable systems

      More details

      4 1976 - Present

      Grant type:Competitive

      researchmap

    • Algebraic analysis of integrable models

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      More details

      4 2011 - 3 2015

      Grant type:Competitive

      Grant amount:\1900000 ( Direct Cost: \1330000 、 Indirect Cost:\570000 )

      researchmap

    • 量子可積分系の代数解析的研究

      日本学術振興会  科学研究費助成事業 

      More details

      4 2008 - 3 2011

      Grant type:Competitive

      Grant amount:\8200000 ( Direct Cost: \5740000 、 Indirect Cost:\2460000 )

      過去数年の共同研究により、代表的な1次元可積分スピン鎖であるXXZモデルの全く一般の相関関数に対する代数的な表示を得た。本研究課題ではさらに有限温度を含む一般化、連続極限における場の理論の研究を目指す。平行して共形場理論、特にその指標の組み合わせ的研究を継続する。

      researchmap

    • 量子可積分系の研究:代数構造と相関関数

      日本学術振興会  科学研究費助成事業 

      More details

      4 2006 - 3 2008

      Grant type:Competitive

      Grant amount:\4900000 ( Direct Cost: \3430000 、 Indirect Cost:\1470000 )

      XXZ模型の相関関数に対する代数的研究を継続した。本研究では、一般の相互作用定数の値において、従来知られていなかったフェルミオンの構造を見いだし、交換関係の証明とそれを用いた相関関数の表示を確立した。

      researchmap