Holomorphic \(H\)-spherical distribution vectors in principal series representations

DOI10.1007/s00222-004-0376-1zbMath1062.22031arXivmath/0304175OpenAlexW2025875576MaRDI QIDQ706138

Bernhard Krötz, Simon G. Gindikin, Gestur Olafsson

Publication date: 2 February 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304175

zbMATH Keywords

Hardy spacespherical principal seriesnon-compactly causal symmetric spaceholomorphic H-spherical distribution vector

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) (H^p)-spaces (42B30) Differential geometry of symmetric spaces (53C35)

Related Items (5)

Horospherical transform on real symmetric varieties: kernel and cokernel ⋮ The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula ⋮ Reflection positivity on spheres ⋮ Corner view on the crown domain ⋮ Partial Poisson transforms on \(SU(n, n)/SL(n, \mathbb{C}) \times \mathbb{R}_+^\ast\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs. (Some properties of spherical representations of reductive symmetric spaces)
• Fourier and Poisson transformation associated to a semisimple symmetric space
• Plancherel formula for reductive symmetric spaces
• The orbits of affine symmetric spaces under the action of minimal parabolic subgroups
• The most continuous part of the Plancherel decomposition for a reductive symmetric space
• Fourier transforms on a semisimple symmetric space
• The \(c\)-function for non-compactly causal symmetric spaces
• Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum
• \(H\)-fixed distribution vectors for generalized principal series of reductive symmetric spaces and meromorphic continuation of Eisenstein integrals
• On Stein extensions of real symmetric spaces
• Holomorphic extensions of representations. I: Automorphic functions
• The Plancherel theorem for biinvariant Hilbert spaces
• Holomorphic extensions of representations. II: Geometry and harmonic analysis
• Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

This page was built for publication: Holomorphic \(H\)-spherical distribution vectors in principal series representations