Representations of SL(2) near the identity

Abstract: The character of an admissible representation $\pi$ of a $p$-adic group $G$ can be expressed, in a neighbourhood of the identity, as a linear combination of functions arising from the finitely many nilpotent orbits. In this talk, we propose an interpretation of the local character expansion as branching rules of the restriction of $\pi$ to a compact open subgroup and illustrate this explicitly with the example of $\mathrm{SL}(2).$

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.