Relative Representation Theory of Reductive Groups Over Close Local fields with Applications to Gelfand Pairs

SHORT TALKS BY POSTDOCTORAL MEMBERS
Topic:Relative Representation Theory of Reductive Groups Over Close Local fields with Applications to Gelfand Pairs
Speaker:Dmitri Gourevich
Affiliation:Member, School of Mathematics
Date:Friday, September 25
Time/Room:2:00pm - 3:00pm/S-101

First I will present a geometric method, due to Kazhdan, of approximating representation theory of reductive groups over local fields of positive characteristic (like F_p(t)) with representation theory of reductive groups over local fields of zero characteristic (like the field Q_p of p-adic numbers). Then I will present a generalization of this method to "representation theory of pairs of groups", due to Aizenbud, Avni and myself. As an application we show that (GL(n+1,F),GL(n,F)) is a strong Gelfand pair for all local fields F of positive characteristic. This means that the restriction to GL(n,F) of every irreducible smooth representation of GL(n+1,F) "decomposes" with multiplicity one. We use our method to deduce this from the zero characteristic case, which was proven two years ago by Aizenbud, myself, Rallis and Schiffmann.