Proc. Japan Acad. Ser. A Math. Sci. 98 (3), 19-24, (March 2022) DOI: 10.3792/pjaa.98.004
KEYWORDS: branching law, multiplicity, Reductive group, symmetric pair, visible action, spherical variety, 22E46, 22E45, 53D50, 58J42, 53C50
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 $G'$.