Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

In their study of the equivariant K-theory of the generalized flag varieties<br />
$G/P$, where $G$ is a complex semisimple Lie group, and $P$ is a parabolic<br />
subgroup of $G$, Lenart and Postnikov introduced a combinatorial tool, called<br />
the alcove paths model. It provides a model for the highest weight crystals<br />
with dominant integral highest weights, generalizing the model by semistandard<br />
Young tableaux. In this paper, we prove a simple and explicit formula<br />
describing the crystal isomorphism between the alcove paths model and the<br />
Gelfand-Tsetlin patterns model for type $A$.

DOI： 10.1007/s00026-021-00544-5

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

DOI： 10.1016/j.jalgebra.2021.02.023

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In this paper, we study basic properties of global $\jmath$-crystal bases for<br />
integrable modules over a quantum symmetric pair coideal subalgebra<br />
$\mathbf{U}^{\jmath}$ associated to the Satake diagram of type AIII with even<br />
white nodes and no black nodes. Also, we obtain an intrinsic characterization<br />
of the $\jmath$-crystal bases, whose original definition is artificial.

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We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the<br />
tensor product of a based $\textbf{U}^{\imath}$-module and a based<br />
$\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used<br />
to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category<br />
$\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main<br />
result in [BW13] (arXiv:1310.0103).

DOI： 10.1007/s00222-018-0801-5

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Publishing type：Research paper (scientific journal)  

We establish a three-parameter Schur duality between the affine Hecke algebra<br />
of type C and a coideal subalgebra of quantum affine $\mathfrak{sl}_n$. At the<br />
equal parameter specializations, we obtain Schur dualities of types BCD.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society  

We establish a Schur-type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with two parameters. We identify the ı-canonical basis on the tensor product of the natural representation with Lusztig’s canonical basis of the type B Hecke algebra with unequal parameters associated to a weight function.

DOI： 10.1090/proc/13749

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

In 1980, Lusztig introduced the periodic Kazhdan Lusztig polynomials, which are conjectured to have important information about the characters of irreducible modules of a reductive group over a field of positive characteristic, and also about those of an affuae Kac Moody algebra at the critical level. The periodic Kazhdan Lusztig polynomials can be computed by using another family of polynomials, called the periodic R-polynomials. In this paper, we prove a (closed) combinatorial formula expressing periodic R-polynomials in terms of the "doubled" Bruhat graph associated to a finite Weyl group and a finite root system. (C) 2016 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jcta.2016.12.008

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Publishing type：Research paper (scientific journal)  

We study the representation theory of a quantum symmetric pair<br />
$(\mathbf{U},\mathbf{U}^{\jmath})$ with two parameters $p,q$ of type AIII, by<br />
using highest weight theory and a variant of Kashiwara&#039;s crystal basis theory.<br />
Namely, we classify the irreducible $\mathbf{U}^{\jmath}$-modules in a suitable<br />
category and associate with each of them a basis at $p=q=0$, the<br />
$\jmath$-crystal basis. The $\jmath$-crystal bases have nice combinatorial<br />
properties as the ordinary crystal bases do.

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Presentation type：Oral presentation (invited, special)  

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Event date： 23 10 2023 - 27 10 2023

Presentation type：Oral presentation (general)  

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Event date： 7 2 2023 - 17 2 2023

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Event date： 13 9 2022 - 16 9 2022

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Event date： 25 6 2021 - 28 6 2021

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Event date： 5 10 2020 - 8 10 2020

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Event date： 1 9 2020 - 4 9 2020

Presentation type：Oral presentation (invited, special)  

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Event date： 14 7 2020 - 15 7 2020

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

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Language：English   Presentation type：Oral presentation (general)  

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

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Language：English   Presentation type：Oral presentation (general)  

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Language：English   Presentation type：Oral presentation (general)  

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

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

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

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Oral presentation (general)  

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Language：Japanese   Presentation type：Oral presentation (general)  

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