Finite multiplicity theorems for induced representations of semisimple Lie groups and their applications to generalized Gelfand-Graev representations
type: Item
instance of: scholarly article
title: Finite multiplicity theorems for induced representations of semisimple Lie groups and their applications to generalized Gelfand-Graev representations
zbMATH Open document ID: 0636.22010
author: Hiroshi Yamashita
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: The author announces results whose proofs are to appear elsewhere. They concern finite multiplicity results for induced representations in the following setting. Let G be a real semisimple Lie group with Cartan involution \(\theta\), let \(Q=LN\) be a parabolic subgroup with \(\theta\)- stable Levi component L, suppose that L carries an involution \(\sigma\) which commutes with \(\theta| L\), and let H be an open subgroup of its group of fixed points; thus L/H is a reductive symmetric space. One of the results announced is: if \(\zeta\) is a representation of HN with finite multiplicities, then \(C^{\infty}IND^ G_{HN}(\zeta)\) also has the finite multiplicity property. In the second half of the paper these results are applied to generalized Gelfand-Graev representations associated with irreducible Hermitian symmetric spaces.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 4036095
zbMATH Keywords: induced representations
zbMATH Keywords: real semisimple Lie group
zbMATH Keywords: Cartan involution
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: Levi component
zbMATH Keywords: finite multiplicity property
zbMATH Keywords: Gelfand-Graev representations
zbMATH Keywords: irreducible Hermitian symmetric spaces
MaRDI profile type: Publication
full work available at URL: pjaa.63.153
OpenAlex ID: W2030936253
Wikidata QID: Q115219943
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DOI: 10.3792/PJAA.63.153
description: scientific article; zbMATH DE number 4036095