Bounded multiplicity theorems for induction and restriction

Abstract

We prove a geometric criterion for the bounded multiplicity property of "small" infinite-dimensional representations of real reductive Lie groupsin both induction and restrictions. Applying the criterion to symmetric pairs, we give a full description of the triples $H\subset G\supset G^{\prime }$ such that any irreducible admissible representations of $G$ with $H$-distinguished vectors have the bounded multiplicity property when restricted to the subgroup $G^{\prime }$. This article also completes the proof of the general results announced in the previous paper [Adv. Math. 2021, Section 7].

To appear in Journal of Lie Theory

References in corpus (3)

• Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)
• Tempered homogeneous spaces III
• A generalization of the Kobayashi-Oshima uniformly bounded multiplicity theorem

Cited by in corpus (2)

• Generating operators of symmetry breaking -- from discrete to continuous
• Recent advances in branching problems of representations