We give a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional representations of real reductive Lie groups in both induction and restrictions.
In particular, for a reductive symmetric pair $(G,H)$, we determine the reductive subgroups $G'$ having the property that any irreducible $H$-distinguished admissible representations of $G$ are of bounded multiplicity when restricted to $G'$.
"Multiplicity in restricting small representations." Proc. Japan Acad. Ser. A Math. Sci. 98 (3) 19 - 24, March 2022. https://doi.org/10.3792/pjaa.98.004