PIMS Speaker Series (Part I): Peter Schneider

  • Date: 10/17/2012
  • Time: 04:00
Peter Schneider

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.


Other Information: 

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

Location: ESB 2012