Algebraic structures of Makarevič spaces. I
type: Item
instance of: scholarly article
title: Algebraic structures of Makarevič spaces. I
zbMATH Open document ID: 0894.22004
DOI: 10.1007/BF01237837
published in: Transformation Groups
publication date: 1998-09-08T00:00:00Z
review text: A Makarevič space is a reductive symmetric space \(X=G/H\) which can be realized as an open symmetric orbit in the conformal compactification of a semisimple Jordan algebra. Recently Makarevič spaces with a causal structure have attracted interest because of the Hardy spaces of holomorphic functions one can construct on certain closely related open domains \(\Xi\) in the complex conformal compactification. In the present paper the author studies the Jordan algebraic description of \(X\) and \(\Xi\). A particular role is played by the Bergman operator, which is an operator valued polynomial generalizing the canonical factor of automorphy associated to a Hermitian symmetric domain, and which yields simple and useful descriptions of \(X\) and \(\Xi\) as well as the invariant measure on \(X\).
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 17C30
zbMATH DE Number: 1139664
zbMATH Keywords: conformal group
zbMATH Keywords: Makarevič space
zbMATH Keywords: symmetric space
zbMATH Keywords: Jordan algebra
zbMATH Keywords: Bergman operator
author: Wolfgang Bertram
reviewed by: Joachim Hilgert
MaRDI profile type: Publication
cites work: Q4332328
cites work: Q4861320
cites work: Q4887316
cites work: Q4693080
cites work: Function spaces on the Ol'shanskiĭ semigroup and the Gel'fand-Gindikin program
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description: scientific article; zbMATH DE number 1139664