Unitary Representations and the Langlands Classification

Abstract: Let $G(k)$ be the $k$-points of a connected reductive algebraic group defined over a local field $k$. A fundamental unsolved problem in representation theory and harmonic analysis is to classify the set of irreducible unitary representations of $G(k)$. The Langlands classification provides a (partly conjectural) description of the much larger set of irreducible admissible representations of $G(k)$ in terms of sheaves on a space of Langlands parameters. But what does this classification tell us about unitary representations? In this talk, I will explain what is known in general about the answer to this question.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Canadian Rockies Representation Theory

Series comments: Topics include, but are not limited to, geometric and categorical aspects of the Langlands Programme. Please write to Jose Cruz for zoom instructions.