Centers and centralizers in (double) affine Hecke algebras

Abstract: The affine Hecke algebra and its center are important objects of study in combinatorial, geometric and categorical representation theory. In this talk, I will discuss a new commutative subalgebra of the affine Hecke algebra of type A, which arises from a centralizer construction in the double affine Hecke algebra. This subalgebra contains the center, and it admits a canonical basis akin to the Kazhdan-Lusztig basis of the affine Hecke algebra. I will explain how the canonical basis can be used as a tool to compute composition multiplicities in Gaitsgory's central sheaves on affine flag manifolds.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.