Topologically irreducible representations of the Schwartz-algebra of a nilpotent Lie group
type: Item
instance of: scholarly article
title: Topologically irreducible representations of the Schwartz-algebra of a nilpotent Lie group
zbMATH Open document ID: 0664.43002
DOI: 10.1007/BF01188525
author: Jean Ludwig
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Let N be a connected, simply connected nilpotent Lie group and let S(N) be its Schwartz-algebra. Let E be a locally convex topological vector space and let T be a continuous topologically irreducible representation of S(N) on E. We show that the restriction of T to the subspace \(E^{\infty}=T(S(N))E\) of E is algebraically irreducible and that the kernel ker T of T is of the form ker \(\pi\), where \(\pi\) is an irreducible unitary representation of S(N). We extend thus to general spaces E, using a new proof, the results of \textit{F. Du Cloux} [Représentations tempérées des groupes de Lie nilpotents (Preprint 1987)], who treated the case of Fréchet spaces E.
reviewed by: Jean Ludwig
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 22E27
zbMATH DE Number: 4086265
zbMATH Keywords: simply connected nilpotent Lie group
zbMATH Keywords: Schwartz-algebra
zbMATH Keywords: locally convex topological vector space
zbMATH Keywords: irreducible representation
zbMATH Keywords: unitary representation
Wikidata QID: Q115393946
MaRDI profile type: Publication
cites work: Q4173774
cites work: Jets de fonctions differentiables sur le dual d'un groupe de Lie nilpotent. (Jets of differentiable functions on the dual of a nilpotent Lie group)
cites work: Représentations tempérées des groupes de Lie nilpotents. (Tempered representations of nilpotent Lie groups)
cites work: A functional calculus for Rockland operators on nilpotent Lie groups
cites work: On a connection between nilpotent groups and oscillatory integrals associated to singularities
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description: scientific article; zbMATH DE number 4086265