Bounded multiplicity theorems for induction and restriction

Kavli Affiliate: Toshiyuki Kobayashi

| First 5 Authors: Toshiyuki Kobayashi, , , ,

| Summary:

We prove a geometric criterion for the bounded multiplicity property of
"small" infinite-dimensional representations of real reductive Lie groupsin
both induction and restrictions.
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 $G’$.
This article also completes the proof of the general results announced in the
previous paper [Adv. Math. 2021, Section 7].

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