The Plancherel decomposition for a reductive symmetric space. I: Spherical functions

DOI10.1007/s00222-004-0431-yzbMath1078.22012arXivmath/0107063OpenAlexW3099248809MaRDI QIDQ2574955

Henrik Schlichtkrull, Erik P. van den Ban

Publication date: 5 December 2005

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

Full work available at URL: https://arxiv.org/abs/math/0107063

zbMATH Keywords

spherical functionsreductive symmetric spacePlancherel decomposition

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46)

Related Items (16)

Spectrum of semisimple locally symmetric spaces and admissibility of spherical representations ⋮ Cusp forms for reductive symmetric spaces of split rank one ⋮ Radon transformation on reductive symmetric spaces: support theorems ⋮ Classification of reductive real spherical pairs. I: The simple case ⋮ \(K\)-invariant cusp forms for reductive symmetric spaces of split rank one ⋮ On the little Weyl group of a real spherical space ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ Geometric analysis on small unitary representations of \(\text{GL}(N, \mathbb R)\) ⋮ The infinitesimal characters of discrete series for real spherical spaces ⋮ Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum ⋮ Wave front sets of reductive Lie group representations II ⋮ Normalizations of Eisenstein integrals for reductive symmetric spaces ⋮ Cuspidal discrete series for semisimple symmetric spaces ⋮ Cuspidal integrals for \(\mathrm{SL}(3) / K_\epsilon\) ⋮ The Plancherel decomposition for a reductive symmetric space. II: Representation theory ⋮ Branching laws for small unitary representations of GL(n, ℂ)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of matrix coefficients of admissible representations
• A Paley-Wiener theorem for real reductive groups
• Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula
• Plancherel formula for reductive symmetric spaces
• Intertwining operators for semisimple groups. II
• Discrete series for semisimple symmetric spaces
• Harmonic analysis on real reductive groups. I: The theory of the constant term
• On the functional equations satisfied by Eisenstein series
• Harmonic analysis on real reductive groups. III: The Maass-Selberg relations and the plancherel formula
• Harmonic analysis on real reductive groups. II: Wave-packets in the Schwartz space
• Harmonic analysis on real reductive groups
• Fourier transform on the Schwartz space of a reductive symmetric space
• Meromorphic basis of \(H\)-invariant distribution vectors for generalized principal series of reductive symmetric spaces: Functional equation
• The most continuous part of the Plancherel decomposition for a reductive symmetric space
• Orbital functions on \(G_C/G_R\). Inversion formula of orbital integrals and Plancherel formula
• The action of intertwining operators on spherical vectors in the minimal principal series of a reductive symmetric space
• Truncation for reductive symmetric spaces
• Fourier transforms on a semisimple symmetric space
• Fourier inversion on a reductive symmetric space
• The principal series for a reductive symmetric space. II: Eisenstein integrals
• Wave packets in the Schwartz space of a reductive symmetric space
• Eisenstein integrals for reductive symmetric spaces: Temperedness, majorations. Small \(B\)-matrix
• The surjectivity of invariant differential operators on symmetric spaces. I
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• The Plancherel decomposition for a reductive symmetric space. II: Representation theory
• The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
• Spherical Functions on a Semisimple Lie Group, I
• Canonical Extensions of Harish-Chandra Modules to Representations of G
• Terme constant des fonctions tempérées sur un espace symétrique réductif.
• A PALEY–WIENER THEOREM FOR DISTRIBUTIONS ON REDUCTIVE SYMMETRIC SPACES

This page was built for publication: The Plancherel decomposition for a reductive symmetric space. I: Spherical functions