Emmy-Noether-Seminar

Branching laws for unitary representations of rank one real reductive groups

Jan Frahm

Abstract: Branching laws describe the decomposition of an irreducible representation of a group into irreducible representations for a subgroup. For compact groups one can always decompose unitary representations discretely into direct sums of irreducibles, whereas for non-compact real reductive groups such as GL(n,R) the decomposition will usually involve a continuous part given by a direct integral of irreducible unitary representations. I will try to explain how such decompositions can be obtained in the context of rank one groups, and how they depend on the parameters of the representations.