Branching problems of unitary representations

Abstract

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions). Basic theory and new perspectives of admissible restrictions are presented from both analytic and algebraic view points. We also discuss some applications of admissible restrictions to modular varieties and $L^p$-harmonic analysis.

Cited by in corpus (4)

• Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs
• Algebraic analysis of minimal representations
• Admissible restrictions of irreducible representations of reductive Lie groups: symplectic geometry and discrete decomposability
• Cramped subgroups and generalized Harish-Chandra modules