GRANT Seminar

Let G be a connected reductive group over a p-adic field. Kazhdan and Lusztig established an isomorphism between the extended affine Hecke algebra of G and certain equivariant K-group of the Steinberg variety of the Langlands dual group of G. This isomorphism plays a crucial role in Kazhdan-Lusztig's proof of the Deligen-Langlands conjecture, which can be viewed as the tamely ramified version of the local Langlands conjecture. In the equal characteristic setting, Bezrukavnikov studied the categorification of this isomorphism and proved an equivalence between two geometric realizations of the affine Hecke algebra. I will discuss an ongoing joint project with Bando, Gleason, and Lourenço on an explicit approach to establish Bezrukavnikov's equivalence in mixed characteristics. The key ingredient is the mixed-characteristic central functor established in a joint work with Anschütz, Lourenço, and Wu