## PIMS Speaker Series (Part I): Peter Schneider

- Date: 10/17/2012
- Time: 04:00

University of British Columbia

Iwahori-Hecke algebras are Gorenstein

In the local Langlands program the (smooth) representation theory

of p-adic reductive groups G in characteristic zero plays a key role. For any

compact open subgroup K of G there is a so called Hecke algebra H(G,K). The

representation theory of G is equivalent to the module theories over all these

algebras H(G,K). Very important examples of such subgroups K are the Iwahori

subgroup and the pro-p Iwahori subgroup. By a theorem of Bernstein the Hecke

algebras of these subgroups (and many others) have finite global dimension.

In recent years the same representation theory of G but over

an algebraically closed field of characteristic p has become more and more important.

But little is known yet. Again one can define analogous Hecke algebras. Their

relation to the representation theory of G is still very mysterious. Moreover

they are no longer of finite global dimension. In joint work with R. Ollivier

we prove that over any field the algebra H(G,K), for K the (pro-p) Iwahori

subgroup, is Gorenstein.

This is part one of a two part series. (Part II on October 23rd)

Location: ESB 2012