Speaker: Prof Jeff Adler, from American University, USA

Title:  Representations of p-adic groups: Reducing general problems to depth-zero problems.

Abstract:  Suppose that G is a connected reductive group over a nonarchmidean local field F.  The Bernstein decomposition expresses the category of smooth representations of G(F) has a (usually infinite) product of subcategories.  It has long been known that each of these subcategories is equivalent to the category of modules over some algebra.  We will show that, up to isomorphism, only finitely many algebras arise, and will describe their structure.  As a corollary, each such subcategory is equivalent to a category of “depth-zero” representations of a smaller group.  I will not assume that the audience already knows what “depth-zero” means, or why it matters.