On the Discrete Series of Generalized Stiefel Manifolds

DOI10.2307/2154675zbMath0790.22008OpenAlexW4235391389MaRDI QIDQ4277296

Jian-Shu Li

Publication date: 22 June 1994

Full work available at URL: https://doi.org/10.2307/2154675

zbMATH Keywords

irreducible unitary representationshomogeneous spaceoscillator representationreductive dual pairsleft regular representationgeneralized Stiefel manifold

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Harmonic analysis on homogeneous spaces (43A85) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (1)

Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups

Cites Work

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• Correspondance de Howe pour les paires reductives duales: Quelques calculs dans le cas archimédien. (Howe correspondence for dual reductive pairs: Some calculations in the Archimedean case)
• Singular unitary representations of classical groups
• The local structure of characters
• Primitive ideals and orbital integrals in complex classical groups
• A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group
• Discrete spectrum of the reductive dual pair \((\mathrm{O}(p,q),\mathrm{Sp}(2m))\)
• Restriction of the principal series of \(\mathrm{SL}(n,\mathbb C)\) to some reductive subgroups
• Holomorphic discrete series for the real symplectic group
• Unitary Representations of Reductive Lie Groups. (AM-118)
• Transcending Classical Invariant Theory
• Weil representation. I. Intertwining distributions and discrete spectrum
• Singular unitary representations and discrete series for indefinite Stiefel manifolds 𝑈(𝑝,𝑞;𝐹)/𝑈(𝑝-𝑚,𝑞;𝐹)

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