题目：Graded dimensions and cocenters of the cyclotomic KLR algebras
摘要：
Given a symmetric group Snand 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[Sn]. 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[Sn] 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.
