Affine matrix-ball construction and asymptotic Hecke algebras

Pavlo Pylyavskyy (University of Minnesota)

Wednesday 13th May 16:00-17:00
Maths 311B

Abstract

Left and right cells are a crucial ingredient in the work of Kazhdan and Lusztig on the representation theory of Hecke algebras. In affine type A, Shi showed that left and right cells correspond to tabloids. I will describe a combinatorial algorithm, called the affine matrix-ball construction, which associates to any element of the affine symmetric group a pair of tabloids corresponding to its left and right cells, together with a dominant weight. Asymptotic Hecke algebras isolate the leading-order structure of the Hecke algebra as the parameter approaches infinity. I will explain how the affine matrix-ball construction can be used to give a canonical presentation of the asymptotic Hecke algebra. The talk is based on joint work with Michael Chmutov, Dongkwan Kim, Joel Lewis, and Elena Yudovina. 

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