T. Kobayashi. Bounded multiplicity theorems for induction and restriction. Journal of Lie Theory 32 (2022), 197-238, arXiv: 2109.14424.

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 HGG' 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].

arXiv | preprint version(pdf) ]

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© Toshiyuki Kobayashi