T. Kobayashi. Multiplicity in restricting small representations. Proceedings of Japan Academy, Ser. A 98 (2022), pp.19-24. DOI: 10.3792/pjaa.98.004

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 $G'$.

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