Representations, characters, and spherical functions associated to causal symmetric spaces
type: Item
instance of: scholarly article
title: Representations, characters, and spherical functions associated to causal symmetric spaces
zbMATH Open document ID: 0949.22013
author: Joachim Hilgert
author: Bernhard Krötz
published in: Journal of Functional Analysis
publication date: 2000-12-03T00:00:00Z
review text: In the paper under review the authors study \(H\)-spherical unitary highest weight representations associated to a compactly casual symmetric space \(G/H\). Using these results they prove estimates for the corresponding spherical functions of the dual noncompact casual symmetric space \(G^c/H^c\), which are useful in determining the spectra of the associated weighted Bergman spaces.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1416401
zbMATH Keywords: unitary highest weight representations
zbMATH Keywords: compactly casual symmetric space
zbMATH Keywords: spherical functions
zbMATH Keywords: Bergman spaces
reviewed by: Jing-Song Huang
MaRDI profile type: Publication
full work available at URL: jfan.1999.3467
OpenAlex ID: W2017484377
cites work: \(H\)-fixed distribution vectors for generalized principal series of reductive symmetric spaces and meromorphic continuation of Eisenstein integrals
cites work: Q3318972
cites work: Spherical functions on ordered symmetric spaces
cites work: Q3829998
cites work: Q3897665
cites work: Q3331943
cites work: Weighted Bergman spaces associated with causal symmetric spaces
cites work: Positive definite spherical functions on Olshanskii domains
cites work: Q3203515
cites work: On Hardy and Bergman spaces on complex Ol'shanskiĭ semigroups
cites work: Q4893911
cites work: Spherical representations and mixed symmetric spaces
cites work: Polar and Ol'shanskii decompositions.
cites work: Q5565588
cites work: Q4867160
cites work: Square integrable highest weight representations
cites work: Holomorphy and convexity in Lie theory
cites work: The holomorphic discrete series for affine symmetric spaces. I
cites work: Q3994337
DOI: 10.1006/JFAN.1999.3467
description: scientific article; zbMATH DE number 1416401