The isotropy representation for homogeneous Siegel domains
type: Item
instance of: scholarly article
title: The isotropy representation for homogeneous Siegel domains
zbMATH Open document ID: 0592.32025
author: J. E. D'Atri
author: Yan Da Zhao
author: Josef F. Dorfmeister
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The authors study relations between homogeneous Siegel domains (equivalently, homogeneous bounded domains) and different types of homogeneous spaces. As the main result they give new characterizations of symmetric domains among the class of homogeneous Siegel domains. Let D be a homogeneous Siegel domain, G the identity component of the automorphism group of D and K the isotropy subgroup at a point b of D. Then D is symmetric if and only if at least one of the following conditions is satisfied: a) The almost complex structure map on the tangent space \(T_ bD\) is in the image of the infinitesimal isotropy representation, b) There exist no nontrivial G-invariant vector fields, c) The algebra of G- invariant differential operators on D is commutative, d) The isotropy group acts transitively on the Shilov boundary, e) There exists a vector field X in the center of the isotropy algebra at b of \(D\subset {\mathbb{C}}^ n\) so that the differential of X is invertible as a linear transformation on \({\mathbb{C}}^ n\).
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 3950989
zbMATH Keywords: Hermitian symmetric space
zbMATH Keywords: homogeneous Siegel domains
zbMATH Keywords: homogeneous bounded domains
zbMATH Keywords: isotropy representation
reviewed by: Zbigniew Olszak
MaRDI profile type: Publication
full work available at URL: pjm.1985.120.295
OpenAlex ID: W1982096898
DOI: 10.2140/PJM.1985.120.295
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description: scientific article; zbMATH DE number 3950989