1/29 at 17:30 in 507

Roman Bezrukavnikov

Title : Commuting pairs and invariant distributions

Abstract:  

Pairs of commuting matrices (where one is invertible and the other one is nilpotent), as well as the obvious generalization for a reductive group, arise as points of the inertia stack of the space of unipotent local Langlands parameters. This leads to identification of (a version of) the K-group of this stack with a subspace in invariant distributions on the Langlands dual p-adic group, with applications to endoscopy and character sheaves on the loop group.

An interesting feature observed here is that the space of invariant distributions splits as a direct sum over geometric Langlands parameters (a.k.a. nilpotent orbits). This phenomenon is closely related to asymptotic affine Hecke algebra defined by Lusztig and generalized by Braverman and Kazhdan.

The talk is based on joint works with Ciubotaru, Kazhdan and Varshavsky (in progress) and with Karpov and Krylov."