# Affine Hecke algebras, Langlands duality and geometric structure

### Roger Plymen (Manchester)

Wednesday 13th February, 2008 16:00-17:00 214

#### Abstract

I will begin with Langlands duality, the origin (in the local Langlands conjecture) of the Langlands-Deligne-Lusztig parameters (t,u,\rho), and the concept of an L-packet. I'll move on to affine Hecke algebras H(W,q). Each parameter $t$ is the central character of an induced H(W,q)-module. I'll define the extended quotient, and describe a (conjectural) geometric structure for the set of simple H(W,q)-modules. This conjecture was inspired by the cyclic homology of Alain Connes. All this will be illustrated by the affine Hecke algebra attached to the exceptional group G_2. The asymptotic algebra $J$ will also feature. [Joint work with Anne-Marie Aubert and Paul Baum]