Sur les caractères des groupes de Lie résolubles. (On characters of soluble Lie groups.)
type: Item
instance of: scholarly article
title: Sur les caractères des groupes de Lie résolubles. (On characters of soluble Lie groups.)
zbMATH Open document ID: 0727.22006
author: Mixalis Anoussis
publication date: 1991-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74917
review text: We consider a connected, solvable, unimodular Lie group G. Let \({\mathfrak g}\) be the Lie algebra of G. Let \({\mathfrak l}\) be in the dual of \({\mathfrak g}\). Under the assumption that \({\mathfrak g}({\mathfrak l})\) is reductive in \({\mathfrak g}\), we construct a map \(\phi \to F_{{\mathfrak l},\phi}\) from D(G) to the space of \(C^{\infty}\) functions on an open dense subset of G(\({\mathfrak l})\). Using this map we give a formula for the trace of the operator n(\({\mathfrak l},G)(\phi)\), where n(\({\mathfrak l},G)\) is the unitary representation of G associated to \({\mathfrak l}\). This formula applies to the square-integrable representations modulo Z(G) of the group G.
reviewed by: Mixalis Anoussis
Mathematics Subject Classification ID: 22E27
Mathematics Subject Classification ID: 43A65
zbMATH DE Number: 4200504
zbMATH Keywords: connected, solvable, unimodular Lie group
zbMATH Keywords: Lie algebra
zbMATH Keywords: trace
zbMATH Keywords: unitary representation
zbMATH Keywords: square-integrable representations
MaRDI profile type: Publication
OpenAlex ID: W2324912714
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DOI: 10.5802/AIF.1247
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4200504