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March 2022 Multiplicity in restricting small representations
Toshiyuki Kobayashi
Proc. Japan Acad. Ser. A Math. Sci. 98(3): 19-24 (March 2022). DOI: 10.3792/pjaa.98.004

Abstract

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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Toshiyuki Kobayashi. "Multiplicity in restricting small representations." Proc. Japan Acad. Ser. A Math. Sci. 98 (3) 19 - 24, March 2022. https://doi.org/10.3792/pjaa.98.004

Information

Published: March 2022
First available in Project Euclid: 4 March 2022

Digital Object Identifier: 10.3792/pjaa.98.004

Subjects:
Primary: 22E46
Secondary: 22E45 , 53C50 , 53D50 , 58J42

Keywords: branching law , multiplicity , Reductive group , spherical variety , symmetric pair , visible action

Rights: Copyright © 2022 The Japan Academy

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Vol.98 • No. 3 • March 2022
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