Seeing representations of a group through the lens of its maximal compact subgroups

Abstract: A classical problem in representation theory is to understand how an irreducible representation of a group decomposes when restricted to its subgroups. Such questions are commonly referred to as branching problems.

In this talk, we will explore the restriction of irreducible smooth representations of the unramified quasi-split unitary group U(1,1) to its hyperspecial maximal compact subgroup K. We will present explicit branching rules in this setting and discuss several applications that arise from having a concrete description of these restrictions.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar