Date : September 30, AM 10:30~11:30, 11:40~12:40 in Seoul Time

AM 09:30~10:30, 10:40~11:40 in Taiwan time

Place : Zoom online

Speaker : Chun-Ju Lai (Academia Sinica)

Title & Abstract

1. Schur-Weyl duality, old and new

In the beginning stage of representation theory, Schur's 1901 thesis on polynomial and rational representations of the general linear groups has played an influential role. A double centralizer property with the symmetric groups (i.e., Weyl groups of type A), now known as the Schur-Weyl duality, has been utilized to study the representation theory of the general linear Lie algebra and of the symmetric groups simultaneously. Interests in Schur's ideas still continue nowadays, in a modern setting. In this talk I will focus on the quantum Schur algebras of type A and go over the connection with the quantum groups via coordinate construction, with the Hecke algebras, and with rational Cherednik algebras.

2. Quantum symmetric pairs and Schur-type dualities

There are various (distinct) generalizations of the theory regarding Schur dualities beyond type A. For finite and affine classical types, the quantum symmetric pairs arise naturally from the double centralizer properties with Hecke algebras of finite and affine classical types. I will talk about a type B/C generalization joint with Nakano and Xiang, as well as an affine type C generalization joint with Fan, Li, Luo, Wang and Watanabe.