Representations, characters, and spherical functions associated to causal symmetric spaces

DOI10.1006/jfan.1999.3467zbMath0949.22013OpenAlexW2017484377MaRDI QIDQ1969448

Bernhard Krötz, Joachim Hilgert

Publication date: 3 December 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3467

zbMATH Keywords

spherical functionsBergman spacesunitary highest weight representationscompactly casual symmetric space

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (2)

Spherical functions on mixed symmetric spaces ⋮ On the meromorphic extension of the spherical functions on noncompactly causal symmetric spaces

Cites Work

• The holomorphic discrete series for affine symmetric spaces. I
• On Hardy and Bergman spaces on complex Ol'shanskiĭ semigroups
• Weighted Bergman spaces associated with causal symmetric spaces
• Spherical functions on ordered symmetric spaces
• \(H\)-fixed distribution vectors for generalized principal series of reductive symmetric spaces and meromorphic continuation of Eisenstein integrals
• Holomorphy and convexity in Lie theory
• Polar and Ol'shanskii decompositions.
• Square integrable highest weight representations
• Spherical representations and mixed symmetric spaces
• Positive definite spherical functions on Olshanskii domains
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