A derived Deligne-Langlands correspondence

Jonas Antor (University of Oxford)

Wednesday 31st January 16:00-17:00 Maths 110

Abstract

Affine Hecke algebras are deformations of group algebras of affine Weyl groups that play an important role in the representation theory of p-adic groups. In their groundbreaking work, Kazhdan and Lusztig found a geometric realization of the affine Hecke algebra using equivariant K-theory. This allowed them to prove the Deligne-Langlands correspondence, a special case of the local Langlands conjecture that gives a geometric parametrization of the irreducible representations of the affine Hecke algebras. In this talk, we will discuss a categorical version of this Deligne-Langlands correspondence that relates (dg-)modules over the affine Hecke algebra with certain derived categories of constructible sheaves. Time permitting, we will also briefly talk about some work in progress that attempts to generalize the geometric realization of affine Hecke algebras to the unequal parameter setting.

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