Analytic continuation of branching laws for unitary representations

Abstract: Branching problems ask for the behaviour of the restriction of an irreducible representation of a group $G$ to a subgroup $H$. In the context of smooth representations of real reductive groups, this typically leads to the study of multiplicities with which an irreducible representation of $H$ occurs as a quotient of an irreducible representation of $G$. Here, both quantitative results such as multiplicity-one theorems and qualitative results such as the Gan-Gross-Prasad conjectures are of interest.

In the context of unitary representations of real reductive groups, one can go a step further and explicitly decompose an irreducible representation of $G$ into a direct integral of irreducible representations of $H$. I will explain how branching laws for unitary representations are related to those in the smooth category, and how one can use an analytic continuation procedure along a principal series parameter to obtain explicit branching laws from certain Plancherel formulas for homogeneous spaces.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID: 863 3902 9748

Zoom password: 831352

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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