| Résume | 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. |
