Updated on 2021/06/22

写真b

 
SAITO Yoshihisa
 
*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*
Professor
Degree
博士(理学) ( 京都大学 )
Research Theme*
  • 無限次元リー代数と量子群の表現論を中心に、可積分系、特殊函数論、組合せ論、有限次元代数の表現論、幾何学的表現論、D-加群の理論などに興味を持っている。

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

    Research Areas

    • Natural Science / Algebra

    Research History

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

      More details

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

      More details

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

      More details

    • 4 2001 - 3 2017 
      The University of Tokyo   Graduate School of Mathematical Sciences

      More details

    • 6 1997 - 3 2001 
      広島大学   理学研究科   助手

      More details

    • 6 1997 - 3 2001 
      Hiroshima University

      More details

    ▼display all

    Education

    • - 3 1997 
      Kyoto University   Graduate School, Division of Natural Science

      More details

      Country: Japan

      researchmap

    • - 3 1997 
      Kyoto University   Graduate School, Division of Natural Science

      More details

      Country: Japan

      researchmap

    Papers

    • Quantized coordinate rings, PBW-type bases and q-boson algebras Peer-reviewed

      Yoshihisa Saito

      JOURNAL OF ALGEBRA453   456 - 491   5 2016

      More details

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

      In [7], Kuniba, Okado and Yamada proved that the transition matrix of a PBW-type basis of the positive-half of the quantized universal enveloping algebra U-q(g) coincides with a matrix of the intertwiner between certain irreducible modules over the quantized coordinate ring A(q)(g) introduced by Soibelman [13]. In the present article, we give a new proof of their result, by using representation theory of the q-boson algebra, and the Drinfeld pairing of U-q(g). (C) 2016 Elsevier Inc. All rights reserved.

      DOI: 10.1016/j.jalgebra.2016.01.007

      researchmap

    • Mirkovic-Vilonen Polytopes and a Quiver Construction of Crystal Basis in Type A Peer-reviewed

      Yoshihisa Saito

      INTERNATIONAL MATHEMATICS RESEARCH NOTICES2012 ( 17 ) 3877 - 3928   2012

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

      In the current paper, we give a quiver theoretical interpretation of Mirkovic-Vilonen (MV) polytopes in type A(n). As a by-product, we give a new proof of the Anderson-Mirkovic conjecture that describes the explicit forms of the actions of lowering Kashiwara operators on the set of MV polytopes.

      DOI: 10.1093/imrn/rnr173

      researchmap

    • Toward Berenstein-Zelevinsky data in affine type A, I: Construction of affine analogs Peer-reviewed

      Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito

      Contemporary of Mathematics565   143 - 184   2012

      More details

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

      researchmap

    • Toward Berenstein-Zelevinsky data in affine type A, II: Expicit description Peer-reviewed

      Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito

      Contemporary of Mathematics565   185 - 216   2012

      More details

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

      researchmap

    • Toward Berenstein-Zelevinsky data in affine type A, III: Proof of the connectedness Peer-reviewed

      Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito

      Symmetries, Integrable Systems and Representations   361 - 402   2012

      More details

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

      researchmap

    • Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to sl(2) Peer-reviewed

      Hiroki Kondo, Yoshihisa Saito

      JOURNAL OF ALGEBRA330 ( 1 ) 103 - 129   3 2011

      More details

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

      We study the tensor structure of the category of finite-dimensional modules of the restricted quantum enveloping algebra associated to sl(2). Tensor product decomposition rules for all indecomposable modules are explicitly given. As a by-product, it is also shown that the category of finite-dimensional modules of the restricted quantum enveloping algebra associated to sl(2) is not a braided tensor category. (C) 2011 Elsevier Inc. All rights reserved.

      DOI: 10.1016/j.jalgebra.2011.01.010

      researchmap

    • Double affine Hecke algebras and elliptic Hecke algberas Peer-reviewed

      Yoshihisa Saito, Midori Shiota

      Representation Theory of Algebraic Groups and Quantum Groups (2010)   297 - 312   2010

      More details

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

      researchmap

    • On Hecke algebras associated with elliptic root systems and the double affine Hecke algebras Peer-reviewed

      Yoshihisa Saito, Midori Shiota

      Publications of the Research Institute of Mathematical Sciences45   845 - 905   2009

      More details

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

      researchmap

    • The rational qKZ equation and shifted non-symmetric Jack polynomials Peer-reviewed

      Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito, Yoshihiro Takeyama

      SIGMA5   2009

      More details

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

      researchmap

    • An introduction to canonical bases Peer-reviewed

      Yoshihisa Saito

      Fields Institute Communications40   431 - 451   2004

      More details

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

      researchmap

    • Crystal bases and quiver varieties Peer-reviewed

      Y Saito

      MATHEMATISCHE ANNALEN324 ( 4 ) 675 - 688   12 2002

      More details

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

      We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One can show that, as a crystal, it is isomorphic to the crystal base of an irreducible highest weight representation of a quantized universal enveloping algebra.

      DOI: 10.1007/s00208-002-0332-6

      researchmap

    • Hirota bilinear forms with 2-toroidal symmetries Peer-reviewed

      Kenji Iohara, Yoshihisa Saito, Minoru Wakimoto

      Physics Letter A254 ( 1-2 ) 37 - 46   1999

      More details

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

      researchmap

    • Notes on differential equations arising from a representation of 2-toroidal Lie algebras Peer-reviewed

      K Iohara, Y Saito, M Wakimoto

      PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT135 ( 135 ) 166 - 181   1999

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

      We will explain how one can obtain the Hirota bilinear forms associated with the homogeneous realization of vertex representations of 2-toroidal Lie algebras of type A(l), D-l, E-l.

      researchmap

    • Quantum toroidal algebras and their vertex representations Peer-reviewed

      Y Saito

      PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES34 ( 2 ) 155 - 177   3 1998

      More details

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

      We construct the vertex representations of the quantum toroidal algebras U-q((sic)l(n-1,tor)). In the classical case the vertex representations are not irreducible. However in the quantum case they are irreducible.

      researchmap

    • Toroidal actions on level 1 modules of $U_q(\widehat{sl}_n)$ Peer-reviewed

      Yoshihisa Saito, Koichi Takemura, Denis Uglov

      Transformation groups3 ( 1 ) 75 - 102   1998

      More details

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

      researchmap

    • Geometric construction of crystal bases Peer-reviewed

      M Kashiwara, Y Saito

      DUKE MATHEMATICAL JOURNAL89 ( 1 ) 9 - 36   7 1997

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:DUKE UNIV PRESS  

      researchmap

    • Quantum toroidal algebras and their vertex representations Peer-reviewed

      Yoshihisa Saito

      Publications of Research Institute for Mathematical Physics   3 1997

      More details

      Language:English   Publishing type:Doctoral thesis  

      researchmap

    • PBW BASIS OF QUANTIZED UNIVERSAL ENVELOPING-ALGEBRAS Peer-reviewed

      Y SAITO

      PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES30 ( 2 ) 209 - 232   3 1994

      More details

      Language:English   Publishing type:Research paper (scientific journal)   Publisher:KYOTO UNIV, PUBLICATIONS RESEARCH INST MATHEMATICAL SCIENCES  

      researchmap

    ▼display all

    Books and Other Publications

    • Algebraic Analysis and Around

      Tetsuji Miwa, Atsushi Matsuo, Toshiki Nakashima, Yoshihisa Saito( Role: Joint editor)

      World Scientific  2009 

      More details

      Language:English Book type:Scholarly book

      researchmap

    Presentations

    • On Elliptic Artin Groups Invited

      MSJ spring meeting 2020, Infinite Analysis  3 2020 

      More details

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

      Venue:Nihon University  

      researchmap

    • Artin groups associated with elliptic root systems Invited International conference

      Yoshihisa Saito

      Conference on Algebraic Representation Theory 2019  11 2019 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Department of Mathematics, National Tsing Hua University (Taiwan).  

      researchmap

    • Elliptic Artin groups Invited International conference

      Yoshihisa Saito

      Arbeitsgruppe Algebra und Zahlentheorie Seminare  10 2019 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Mathematisches Institut, University of Cologue (Germany)  

      researchmap

    • Elliptic Artin groups Invited International conference

      Yoshihisa Saito

      Geometry and Integrable Systems  4 2019 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Institut de Mathéamatiques de Bourgogne (France)  

      researchmap

    • On quantum toroidal algebras associated with arbitrary root systems Invited International conference

      Yoshihisa Saito

      Arbeitsgruppe Algebra und Zahlentheorie Seminare  6 2018 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Mathematisches Institut, University of Cologue (Germany)  

      researchmap

    • On quantum toroidal algebras associated with arbitrary semisimple Lie algebras Invited International conference

      Yoshihisa Saito

      Infinite Analysis 2017  12 2017 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Osaka City University  

      researchmap

    • Quantum groups, quivers and related geometry Invited International conference

      Yoshihisa Saito

      Quantum Field Theory and Subfactors  11 2016 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:UC Berkekey (USA)  

      researchmap

    • On quantum elliptic algebras Invited International conference

      Yoshihisa Saito

      Geometric Representation Theory  10 2016 

      More details

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

      Venue:Kyoto University  

      researchmap

    • On Elliptic Artin Groups Invited International conference

      Yoshihisa Saito

      Shanghai Conference on Representation Theory  12 2015 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Shanghai (China)  

      researchmap

    • Geometric construction of crystal bases and its applications Invited International conference

      Yoshihisa Saito

      Series of Lectures on Representation Theory  10 2015 

      More details

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

      Venue:Tongji University, Shanghai, China  

      researchmap

    • Quantized coordinate rings, PBW bases and q-boson algebras Invited International conference

      Yoshihisa Saito

      Shanghai Workshop on Representation Theory  12 2014 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Tongi University (Shanghai, China)  

      researchmap

    • Quantized coordinate rings, PBW bases and q-boson algebras Invited International conference

      Yoshihisa Saito

      Representation Theory and Related Topics (ICM2014 Satellite Conference)  8 2014 

      More details

      Language:English   Presentation type:Oral presentation (general)  

      Venue:Daegu (Korea)  

      researchmap

    • Realization of crystal bases Invited International conference

      Yoshihisa Saito

      The 2nd mini-symposium on Representation theory  12 2012 

      More details

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

      Venue:Jeju, Korea  

      researchmap

    • On Berenstein-Zelevinsky data in affine type A Invited International conference

      Yoshihisa Saito

      Integrable systems and Representations  12 2011 

      More details

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

      Venue:Lyon, France  

      researchmap

    • Preprojective algebras and crystal bases Invited International conference

      Yoshihisa Saito

      第44回環論および表現論ジンポジウム  9 2011 

      More details

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

      Venue:Okayama University  

      researchmap

    • On Berenstein-Zelevinsky data in affine type A Invited International conference

      Yoshihisa Saito

      Conformal field theories and tensor categories  6 2011 

      More details

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

      Venue:Beijing International Center for Mathematical Research, Beijing University  

      researchmap

    • Mirkovic-Vilonen polytopes and quiver construction of crystal basis in type A Invited International conference

      Yoshihisa Saito

      Representation Theory of Algebraic Groups and Quantum Groups '10  8 2010 

      More details

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

      Venue:Nagoya University  

      researchmap

    • On tensor category arising from representation theory of the restricted quantum universal enveloping algebra associated to sl2 Invited International conference

      Yoshihisa Saito

      Interplay between representation theory and geometry  5 2010 

      More details

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

      Venue:Tsinghua University, Beijing  

      researchmap

    ▼display all

    Research Projects

    • 量子群の幾何学的研究とその応用

      日本学術振興会  科学研究費助成事業 

      More details

      4 2016 - Present

      Grant type:Competitive

      researchmap

    • 量子群および多元環の表現論の幾何学的研究

      日本学術振興会  科学研究費助成事業 

      More details

      4 2012 - 3 2016

      Grant type:Competitive

      researchmap

    • 量子群の幾何学的研究およびその多元環の表現論への応用

      日本学術振興会  科学研究費助成事業 

      More details

      4 2008 - 3 2012

      Grant type:Competitive

      researchmap

    • アフィン量子群の表現論の幾何学的研究

      日本学術振興会  科学研究費助成事業 

      More details

      4 2005 - 3 2008

      Grant type:Competitive

      researchmap

    • 量子群の表現論の幾何学的研究

      日本学術振興会  科学研究費助成事業 

      More details

      4 2002 - 3 2005

      Grant type:Competitive

      researchmap

    • トロイダル代数と可積分系

      日本学術振興会  科学研究費助成事業 

      More details

      4 2000 - 3 2002

      Grant type:Competitive

      researchmap

    • トロイダル代数及び量子トロイダル代数の表現論の研究

      日本学術振興会  科学研究費助成事業 

      More details

      4 1998 - 3 2000

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1997 - 5 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    • ???

      科学研究費助成事業 

      More details

      4 1994 - 3 1997

      Grant type:Competitive

      researchmap

    ▼display all