Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	胡峻教授，北京理工大学
Inviter:	中国科学院数学院学术报告会组委
Title:	Graded dimensions and cocenters of the cyclotomic KLR algebras
Language:	Chinese
Time & Venue:	2024.01.12 10:40-11:50 南楼204教室腾讯会议：534-8268-8299
Abstract:	Given a symmetric group S_n and a field K of positive characteristic, it is a nontrivial question to determine the dimension (not to say a basis) of each block of K[S_n]. In this talk I shall describe some simple closed Lie theoretic formulae for the Z-graded dimensions of the cyclotomic KLR algebras of arbitrary types (which includes the blocks of K[S_n] as special cases). The formula reveals the significance of some new numeric invariants, suggesting that their full role is yet to be fully explored. I will also report our recent work on the cocenters of these cyclotomic KLR algebras of arbitrary types. The talk is based on some joint work with Lei Shi.