\(L^ p\)-analysis on homogeneous manifolds of reductive type and representation theory
type: Item
instance of: scholarly article
title: \(L^ p\)-analysis on homogeneous manifolds of reductive type and representation theory
zbMATH Open document ID: 0883.22015
author: Toshiyuki Kobayashi
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-09-04T00:00:00Z
review text: \(L^p\)-analysis on homogeneous manifolds of reductive type and representation theory are discussed. The main results are: Let \(G\) be a real reductive linear Lie group, \(K\) a maximal compact subgroup of \(G\), and \(\theta\) the corresponding Cartan involution, \(H\) a closed \(\theta\)-stable subgroup of \(G\) with finitely many connected components. There are four sections in this paper: (1) Invariant measures on homogeneous manifolds of reductive type. (2) Irreducible representations in \(L^p(G/H)\). (3) Holomorphic discrete series representations. (4) Some valuable examples are given.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 1057080
zbMATH Keywords: invariant measures
zbMATH Keywords: irreducible representations
zbMATH Keywords: homogeneous manifolds
zbMATH Keywords: real reductive linear Lie group
reviewed by: Su Weiyi
MaRDI profile type: Publication
full work available at URL: pjaa.73.62
OpenAlex ID: W2023198149
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DOI: 10.3792/PJAA.73.62
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description: scientific article; zbMATH DE number 1057080