# Unitary branching laws for real reductive groups

Clemens Weiske (Aarhus University)
Seminar
Thursday, 27 February, 2020 | 11:00–12:00 | Koll. B3 (1535-322)
Contact: Jan Frahm

Let G be a real reductive group, P a minimal parabolic and H a reductive subgroup of G . Unitary branching laws describe how an irreducible unitary representation of G decomposes into a direct integral of irreducible unitary representations of H when restricted to the subgroup H . If the representation is a unitary principal series representation and H has an open orbit on the flag manifold G / P , Mackey theory reduces this problem to the Plancherel formula of a homogeneous space for H which is known in many cases. We will show how to construct branching laws for other unitary representations like complementary series representations from the ones for the unitary principal series by an analytic continuation procedure and show examples for real reductive groups of rank one.

Organised by: SBiM