Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)
type: Item
instance of: scholarly article
title: Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)
zbMATH Open document ID: 0622.22008
DOI: 10.1007/BF01389085
author: Michel Lassalle
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143487
review text: The main theme of this paper is to formulate the problem of determining the relatively invariant measures on a closure of a convex cone in a formally real Jordan algebra and to solve it. Let A be a formally real Jordan algebra whose unit is E. Let \({\mathbb{G}}\) be the connected component of the structure group of A containing the neutral element and let \(\Omega\) be the \({\mathbb{G}}\)-orbit of \(e\in A\). Then the closure \({\bar \Omega}\) decomposes into a finite number of \({\mathbb{G}}\)-orbits. The author proves that each orbit in \(\Omega\) has relatively invariant measures and determines all of them. This contributes to the determination of the Wallach set, which is defined in relation to the unitarization problem of analytic continuation of discrete series.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 17C10
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 4008701
zbMATH Keywords: unitary representation of Lie group
zbMATH Keywords: invariant measures
zbMATH Keywords: convex cone
zbMATH Keywords: formally real Jordan algebra
zbMATH Keywords: structure group
zbMATH Keywords: Wallach set
zbMATH Keywords: unitarization problem
zbMATH Keywords: analytic continuation of discrete series
reviewed by: Masakazu Muro
MaRDI profile type: Publication
cites work: Q5522255
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description: scientific article; zbMATH DE number 4008701