On a class of generalized Gelfand pairs

DOI10.1007/BF01160476zbMath0613.43009OpenAlexW1985235811MaRDI QIDQ1819315

Gerrit Van Dijk

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173806

zbMATH Keywords

pseudo-Riemannian symmetric spacegeneralized Gelfand pairs

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Differential geometry of symmetric spaces (53C35)

Related Items (14)

A new class of Gelfand pairs ⋮ Invariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one ⋮ Functional analytic aspects of non-commutative harmonic analysis ⋮ Discrete series representations with non-tempered embedding ⋮ Invariant functionals on Speh representations ⋮ A partial analog of the integrability theorem for distributions on \(p\)-adic spaces and applications ⋮ Invariant Hilbert subspaces of the oscillator representation ⋮ On some classes of multiplicity free representations ⋮ Some regular symmetric pairs ⋮ Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis's theorem. With an appendix by the authors and Eitan Sayag. ⋮ \((\text O(V\oplus F),\text O(V))\) is a Gelfand pair for any quadratic space \(V\) over a local field \(F\) ⋮ \((\text U(p, q), \text U(p - 1, q))\) is a generalized Gelfand pair ⋮ \((\mathrm{GL}(n+1,\mathbb R),\mathrm{GL}(n,\mathbb R))\) is a generalized Gelfand pair ⋮ Weakly symmetric pseudo-Riemannian nilmanifolds

Cites Work

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• On generalized Gelfand pairs
• Distributions spheriques sur les espaces hyperboliques
• Les espaces symétriques noncompacts
• Distributions Invariant under an Orthogonal Group of Arbitrary Signature.
• On the existence and irreducibility of certain series of representations
• Functional analysis

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