EVENT DETAILS AND ABSTRACT

Title: Geometric structure in the representation theory of p-adic groups
Speaker: Professor Paul Baum
Speaker Info: Penn State
Brief Description:
Special Note:
Abstract:

Let G be a reductive p-adic group. G is locally compact so G has the usual unitary representation theory of locally compact groups. For number theory, Langlands program etc, however, the relevant representations are the smooth representations. This talk states a conjecture --- due to A.M.Aubert, P.Baum and R.Plymen --- which states that the smooth dual of G (i.e. the set of isomorphism classes of irreducible smooth representations of G) is a countable disjoint union of complex affine varieties. These varieties are explicitly identified. The conjecture is very closely connected to work of J.Bernstein and is based on calculations of the periodic cyclic homology of affine Hecke algebras. This talk is algebraic and might be viewed as non-commutative algebraic geometry. However, there is some interaction with the usual unitary representation theory of G.