Analytic continuation of branching laws for unitary representations

2022-05-18 15:00-16:30 Zoom

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.

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