Equivariant derived category of a reductive group as a categorical center

Abstract: There is a classical relationship between representations of the Iwahori-Hecke algebra associated with a Weyl group of a split reductive group G, defined over a finite field, and the (principal series) representations of the corresponding finite group of Lie type. I will discuss a categorification of this relationship in the context of various triangulated categories of constructible sheaves on the group G. In particular, I will present a new approach to connecting the categories of character sheaves to a version of a categorical center of the constructible Hecke category. Based on a joint work with R. Bezrukavnikov, A. Ionov, and Y. Varshavsky.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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