I plan to explain a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional representations of real reductive Lie groups in branching problems.Applying the criterion to symmetric pairs, we give a full description of the triples $H \subset G \supset G'$ such that any irreducible admissible representations of $G$ with $H$-distinguished vectors have the bounded multiplicity property when restricted to the subgroup $G'$.

The precise results are available in [Adv. Math. 2021, Section 7] and arXiv:2109.14424, and I plan to give some flavor.

© Toshiyuki Kobayashi