Representation theory of quantum symmetric pairs and Kazhdan- Lusztig bases

開催日時
2017/10/20 金 16:30 - 18:00
場所
RIMS420号室
講演者
渡邉英也
講演者所属
東工大
概要

In 2013, Huanchen Bao and Weiqiang Wang discovered the
Schur-Weyl-type duality between some quantum symmetric pair coideal
subalgebras $U^{\jmath}$ and the Hecke algebra $H$ (with unequal
parameter) of type B. Namely, they equipped the $d$-th tensor power
of the vector representation $V$ of $U_q(\mathfrak{sl}_n)$ with
a $(U^{\jmath},H)$-bimodule structure which satisfies the double
centralizer property. In this talk, we investigate the bimodule
structure of $V^{\otimes d}$ and see that its $\jmath$-canonical
basis (introduced by Bao and Wang) coincides with its (parabolic)
Kazhdan-Lusztig basis. Time permitting, we will see how this result
relates to the Lusztig's periodic $W$-graphs. This talk is partially
based on a joint work with Bao and Wang.