The Plancherel formula for the line bundles on \(\mathrm{SL}(n + 1, \mathbb{R})/S(\mathrm{GL}(1,\mathbb{R})\times \mathrm{GL}(n, \mathbb{R}))\)

DOI10.1016/S0252-9602(17)30130-3zbMath1399.22016OpenAlexW2772998182MaRDI QIDQ1637015

L. Zhu

Publication date: 7 June 2018

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0252-9602(17)30130-3

zbMATH Keywords

Plancherel formulapseudo-Riemannian symmetric spacespherical distributionsCasimir operatorsPoisson kernels

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (1)

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Cites Work

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• \((\mathrm{GL}(n+1,\mathbb R),\mathrm{GL}(n,\mathbb R))\) is a generalized Gelfand pair
• Spherical distributions on the pseudo-Riemannian space SL(n, \({\mathbb{R}})/GL(n-1,\,{\mathbb{R}})\)
• Distributions spheriques sur les espaces hyperboliques
• Distributions Invariant under an Orthogonal Group of Arbitrary Signature.

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