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. Time permitting, I will also describe ongoing work linking the theory of character sheaves to symmetries of Khovanov-Rozansky homology. Based on joint works with R. Bezrukavnikov, A. Ionov, and Y. Varshavsky.
Equivariant derived category of a reductive group as a categorical center
16.05.2023 13:15 - 14:45
Organiser:
H. Grobner, A. Mellit
Location: