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July 2019 Relationship between orbit decomposition on the flag varieties and multiplicities of induced representations
Taito Tauchi
Proc. Japan Acad. Ser. A Math. Sci. 95(7): 75-79 (July 2019). DOI: 10.3792/pjaa.95.75

Abstract

Let $G$ be a real reductive Lie group and $H$ a closed subgroup. T. Kobayashi and T. Oshima established a finiteness criterion of multiplicities of irreducible $G$-modules occurring in the regular representation $C^{\infty}(G/H)$ by a geometric condition, referred to as \textit{real sphericity}, namely, $H$ has an open orbit on the real flag variety $G/P$. This note discusses a refinement of their theorem by replacing a minimal parabolic subgroup $P$ with a general parabolic subgroup $Q$ of $G$, where a careful analysis is required because the finiteness of the number of $H$-orbits on the partial flag variety $G/Q$ is not equivalent to the existence of $H$-open orbit on $G/Q$.

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Taito Tauchi. "Relationship between orbit decomposition on the flag varieties and multiplicities of induced representations." Proc. Japan Acad. Ser. A Math. Sci. 95 (7) 75 - 79, July 2019. https://doi.org/10.3792/pjaa.95.75

Information

Published: July 2019
First available in Project Euclid: 24 July 2019

zbMATH: 07213562
MathSciNet: MR3983316
Digital Object Identifier: 10.3792/pjaa.95.75

Subjects:
Primary: 22E46
Secondary: 22E45, 53C30

Rights: Copyright © 2019 The Japan Academy

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Vol.95 • No. 7 • July 2019
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