An infinite dimensional version of the Kostant convexity theorem.
type: Item
instance of: scholarly article
title: An infinite dimensional version of the Kostant convexity theorem.
zbMATH Open document ID: 1035.17032
author: Andreas Neumann
published in: Journal of Functional Analysis
publication date: 2003-04-01T00:00:00Z
review text: Let \(L\) be the unitary real form of a classical (infinite dimensional) Lie algebra, \(\mathcal U\) its unitary group, \(H\) a Cartan subspace (that is, a maximal abelian Lie subalgebra which can be simultaneously diagonalized), \(p\) the projection onto \(H\) and \(M\) the Weyl group, which is defined as the quotient \(N/Z,\) where \(N\) is the normalizer and \(Z\) is the centralizer of \(H\) in a Lie group with Lie algebra \(H.\) The group \(M\) operates canonically on \(H.\) The main result of the paper under review is that \(\overline{p(\{ U^\star XU: U\in {\mathcal U}\} )}= \overline{\text{ conv} (M.X)},\) for every \(X\in H.\) This is a generalization of the Kostant Convexity Theorem [\textit{B. Kostant}, Ann. Sci. Éc. Norm. Supér. (4) 6, 413--455 (1973; Zbl 0293.22019)].
reviewed by: José Antonio Cuenca Mira
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 47L70
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1747017
zbMATH Keywords: bounded linear operator
zbMATH Keywords: Weyl group
MaRDI profile type: Publication
full work available at URL: jfan.2000.3739
OpenAlex ID: W2007303931
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DOI: 10.1006/JFAN.2000.3739
description: scientific article; zbMATH DE number 1747017