Q1064505
type: Item
instance of: scholarly article
title: La formule de Poisson-Plancherel pour un groupe de Takiff associé à un groupe de Lie semi-simple à centre fini. (The Poisson-Plancherel formula for a Takiff group associated to a semi-simple Lie group with finite centre)
zbMATH Open document ID: 0575.43005
DOI: 10.1016/0022-1236(84)90075-2
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: The semi-direct product of a semi-simple Lie group with finite centre by its Lie algebra is called a Takiff group. This paper establishes the Plancherel formula for such a group, as conjectured by \textit{M. Vergne} [cf. Ann. Math., II. Ser. 115, 639-666 (1982; Zbl 0501.43006)]. The main technical problem is to define an analogue of orbital integrals which makes sense at singular points, and to calculate its Fourier transform.
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 3919038
zbMATH Keywords: Poisson-Plancherel formula
zbMATH Keywords: Takiff group
zbMATH Keywords: orbital integrals
zbMATH Keywords: Fourier transform
author: Pierre Torasso
reviewed by: Joe Repka
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90075-2
OpenAlex ID: W2081853427
cites work: Q5624172
cites work: Q3954001
cites work: Q3672192
cites work: Fast decreasing functions and characters of real algebraic groups
cites work: Caractères des groupes de Lie
cites work: The plancherel formula for group extensions II
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cites work: Rings of Invariant Polynomials for a Class of Lie Algebras
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cites work: A Poisson-Plancherel formula for semi-simple Lie groups
label: La formule de Poisson-Plancherel pour un groupe de Takiff associé à un groupe de Lie semi-simple à centre fini. (The Poisson-Plancherel formula for a Takiff group associated to a semi-simple Lie group with finite centre)
description: scientific article; zbMATH DE number 3919038