Invariant analytic domains in complex semisimple groups
type: Item
instance of: scholarly article
title: Invariant analytic domains in complex semisimple groups
zbMATH Open document ID: 0867.22004
DOI: 10.1007/BF02549210
published in: Transformation Groups
publication date: 1997-03-23T00:00:00Z
review text: Let \(H_\mathbb{R}\) be a real form of a complex, connected and simply connected, semisimple algebraic group \(H\) with complex conjugation \(\vartheta\). Let \(\Omega\) be the open dense subset of elements \(x\in H\) such that \(x\vartheta (x^{-1})\) is regular semisimple. The paper provides a study of the connected components of \(\Omega\), which are complex analytic domains, and cross-sections of the \(H_\mathbb{R} \times H_\mathbb{R}\) action on these components. This study is motivated by the Gelfand-Gindikin program to construct explicit unitary representations of \(H_\mathbb{R}\) related to complex analytic objects.
reviewed by: Guy Roos
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 994115
zbMATH Keywords: semisimple algebraic group
zbMATH Keywords: Gelfand-Gindikin program
zbMATH Keywords: unitary representations
author: Ralph J. Bremigan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 994115