4 citations · 19 across the 16 of their papers we have counts for
16 papers
Kashiwara--Nakashima tableaux, Gelfand--Tsetlin patterns, and quantum symmetric pairs
Hideya Watanabe
Kashiwara--Nakashima tableaux and Gelfand--Tsetlin patterns of orthogonal type are famous as combinatorial models of the finite-dimensional irreducible representations of the speci…
Integrable modules over quantum symmetric pair coideal subalgebras
Hideya Watanabe
We introduce the notion of integrable modules over quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we…
Symplectic tableaux and quantum symmetric pairs
Hideya Watanabe
We provide a new branching rule from the general linear group to the symplectic group by establishing a simple algorithm which gives ris…
Stability of canonical bases of locally finite type
Hideya Watanabe
We prove the stability conjecture of canonical bases, which was raised by Huanchen Bao and Weiqiang Wang in 2016, for all locally finite types. To this end, we characterize…
Kirillov-Reshetikhin modules and quantum -matrices
Hiroto Kusano, Masato Okado, Hideya Watanabe
From a quantum -matrix of the fundamental representation, we construct one for the Kirillov-Reshetikhin module by fusion construction. Using the crystal theory by the la…
Stability of canonical bases of irreducible finite type of real rank one
Hideya Watanabe
It has been known since their birth in Bao and Wang's work that the canonical bases of quantum groups are not stable in general. In the author's previous work, the…
A new tableau model for irreducible polynomial representations of the orthogonal group
Hideya Watanabe
We provide a new tableau model from which one can easily deduce the characters of finite-dimensional irreducible polynomial representations of the special orthogonal group $SO_n(\m…
Based modules over the quantum group of type AI
Hideya Watanabe
This paper studies classical weight modules over the quantum group of type AI. We introduce the notion of based -modules by gener…
Classical weight modules over quantum groups
Hideya Watanabe
quantum groups are generalizations of quantum groups which appear as coideal subalgebras of quantum groups in the theory of quantum symmetric pairs. In this paper, we defin…
Alcove paths and Gelfand-Tsetlin patterns
Hideya Watanabe, Keita Yamamura
In their study of the equivariant K-theory of the generalized flag varieties , where is a complex semisimple Lie group, and is a parabolic subgroup of , Lenart and…
Global crystal bases for integrable modules over a quantum symmetric pair of type AIII
Hideya Watanabe
In this paper, we study basic properties of global -crystal bases for integrable modules over a quantum symmetric pair coideal subalgebra associated t…
Quantum Schur duality of affine type C with three parameters
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +3
We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine . At the equal parameter special…
Crystal basis theory for a quantum symmetric pair
Hideya Watanabe
We study the representation theory of a quantum symmetric pair with two parameters of type AIII, by using highest weight theory and a varia…
Canonical bases arising from quantum symmetric pairs
Huanchen Bao, Weiqiang Wang
We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical ba…
Multiparameter quantum Schur duality of type B
Huanchen Bao, Weiqiang Wang, Hideya Watanabe
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 2 parameters. We identify the -canonical…
A combinatorial formula expressing periodic -polynomials
Hideya Watanabe, Satoshi Naito
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…