# GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

**Topic: **A Satake Isomorphism mod.p

**Speaker: **Guy Henniart

**Affiliation: **University of Paris-Sud

**Date & Time: **Thursday November 4th, 2010, 2:15pm - 3:15pm

**Location: **S-101

Let F be a locally compact non-Archimedean field, p its residue characteristic and G a connected reductive algebraic group over F . The classical Satake isomorphism describes the Hecke algebra (over the field of complex numbers) of double classes in G with respect to a special maximal compact subgroup K of G . In our setting K is a slightly smaller special parahoric subgroup, we introduce an absolutely irreducible smooth representation of K on a vector field V over a field of characteristic p , and we get a description of an analoguous Hecke algebra with respect to V . We thus generalize work of F. Herzig treating the case of unramified groups G . But in our general situation the Hecke algebra can be non-commutative. (This is joint work with M.-F. VignÃ©ras.)