Sur les caractères des groupes de Lie. (On the characters of Lie groups)
type: Item
instance of: scholarly article
title: Sur les caractères des groupes de Lie. (On the characters of Lie groups)
zbMATH Open document ID: 0679.22009
DOI: 10.1016/0022-1236(87)90083-8
author: Jean-Yves Charbonnel
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: Let G be a Lie group with Lie algebra \({\mathfrak g}\). Let \(\pi\) be a representation of G. The author studies the factor generated by \(\pi\) (G). The main result of the paper is the existence of operators of Hilbert-Schmidt class of the form \(\pi (u^ k*\phi)\) for \(\phi\in {\mathcal D}(G)\) and \(u\in \hat I\), where \(\hat I\) is the intersection of all the primitive ideals of U(\({\mathfrak g})\), containing the kernel I of the infinitesimal representation of U(\({\mathfrak g})\), corresponding to the representation \(\pi\). In the case of the normal factor representation \(\pi\) the author proves the existence of a trace class operator of the form \(\pi\) (\(\phi)\) for some \(\phi\in {\mathcal D}(G)\) relative to the factor generated by \(\pi\) (G).
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 22E27
Mathematics Subject Classification ID: 17B15
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 4112914
zbMATH Keywords: operators of Hilbert-Schmidt class
zbMATH Keywords: primitive ideals
zbMATH Keywords: infinitesimal representation
zbMATH Keywords: normal factor representation
zbMATH Keywords: trace class operator
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90083-8
OpenAlex ID: W1998688305
cites work: Q5662168
cites work: On Homogeneous Affine Spaces of Linear Algebraic Groups
cites work: Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
cites work: Über die Gelfand-Kirillov-Dimension. (On the Gelfand-Kirillov-dimension)
cites work: Q5537437
cites work: Q3941610
cites work: Sur les semi-caractères des groupes de Lie resolubles connexes
cites work: Idéaux primitifs et opérateurs compacts
cites work: Q5531996
cites work: Q5644128
cites work: Q4065692
cites work: Primitive ideals in enveloping algebras
cites work: Q4173774
cites work: Sur les extensions des représentations irréductibles des groupes de Lie nilpotents
cites work: Théorie de Mackey pour les groupes de Lie algébriques
cites work: Q4089001
cites work: Q3222380
cites work: Ideaux primitifs des algèbres enveloppantes
cites work: Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante
cites work: Sur la classification des idéaux primitifs des algèbres enveloppantes
cites work: Fully Reducible Subgroups of Algebraic Groups
cites work: On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
cites work: Analytic vectors
cites work: Action of algebraic groups of automorphisms on the dual of a class of type ${\rm I}$ groups
cites work: Characters of connected Lie groups
cites work: L'injectivite de l'application de Dixmier pour les algèbres de Lie resolubles
cites work: Some rationality questions on algebraic groups
cites work: Faisceaux algébriques cohérents
cites work: Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble
cites work: Q5682517
cites work: Q5682518
description: scientific article; zbMATH DE number 4112914