We prove a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional representations of real reductive Lie groups in both induction and restrictions.Applying the criterion to symmetric pairs, we give a full description of the triples H ⊂ G ⊃ G' such that any irreducible admissible representations of G with H-distinguished vectors have the bounded multiplicity property when restricted to the subgroup G'. This article also completes the proof of the general results announced in the previous paper [Adv. Math. 2021, Section 7].
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© Toshiyuki Kobayashi