The Schwartz space of a general semisimple Lie group. I: Wave packets of Eisenstein integrals
type: Item
instance of: scholarly article
title: The Schwartz space of a general semisimple Lie group. I: Wave packets of Eisenstein integrals
zbMATH Open document ID: 0711.22005
DOI: 10.1016/0001-8708(90)90025-I
author: Rebecca A. Herb
author: Joseph A. Wolf
published in: Advances in Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let G be a semisimple Lie group with infinite center. As in the finite center case, the tempered spectrum of G consists of families of representations induced from cuspidal parabolic subgroups MAN. However the representations of M to be induced are relative discrete series which occur in continuous families. In the reviewed paper the authors construct Schwartz class wave packets of matrix coefficients of induced tempered representations for any connected reductive Lie group G. Note that the authors use the induction not on G but rather on parabolic subgroups of G. This simplifies the constructions. In the special case \(G=M\) the wave packets are exactly the ones constructed in two previous papers [J. Funct. Anal. 73, 1-37 and 38-106 (1987; Zbl 0625.22010 and Zbl 0625.22011)].
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A80
zbMATH DE Number: 4168960
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: tempered spectrum
zbMATH Keywords: cuspidal parabolic subgroups
zbMATH Keywords: relative discrete series
zbMATH Keywords: Schwartz class wave packets
zbMATH Keywords: matrix coefficients
zbMATH Keywords: induced tempered representations
zbMATH Keywords: connected reductive Lie group
Wikidata QID: Q115368963
reviewed by: V. F. Molchanov
MaRDI profile type: Publication
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full work available at URL: 0001-8708(90)90025-i
OpenAlex ID: W1992631560
description: scientific article; zbMATH DE number 4168960