Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs. (Some properties of spherical representations of reductive symmetric spaces)
type: Item
instance of: scholarly article
title: Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs. (Some properties of spherical representations of reductive symmetric spaces)
zbMATH Open document ID: 0662.22007
DOI: 10.1016/0022-1236(88)90002-X
author: Patrick Delorme
author: Erik P. van den Ban
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: The authors study the reductive real Lie group G and the symmetric space G/H. Suppose V is an admissible (\({\mathfrak g},K)\)-module of finite length with a linear functional T which is fixed by \({\mathfrak h}\) and \(H\cap K\). They show that V can be mapped equivariantly into \(C^{\infty}(G/H)\) so that T becomes the pull-back of the Dirac measure at the origin. The proof makes use of the fact that formal power series for matrix coefficients of V satisfy a system of differential equations with regular singularities. The methods begin with work of Casselman and make use of a result of Korevaar and Wiegerinck as well as earlier work appearing in a paper of \textit{P. Delorme} [in Lect. Notes Math. 1243, 108-143 (1987; Zbl 0658.22003)].
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 22E47
zbMATH DE Number: 4081858
zbMATH Keywords: admissible module
zbMATH Keywords: Lie algebra
zbMATH Keywords: reductive real Lie group
zbMATH Keywords: symmetric space
zbMATH Keywords: Dirac measure
reviewed by: Audrey A. Terras
MaRDI profile type: Publication
cites work: Q3766269
cites work: Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula
cites work: Q3860030
cites work: Asymptotic behavior of matrix coefficients of admissible representations
cites work: Q3807446
cites work: Q3714370
cites work: Q5659897
full work available at URL: 0022-1236(88)90002-x
OpenAlex ID: W2002247129
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description: scientific article; zbMATH DE number 4081858