Discrete spectrum of the reductive dual pair \((\mathrm{O}(p,q),\mathrm{Sp}(2m))\)

DOI10.1007/BF01394246zbMath0561.22011OpenAlexW2071341424MaRDI QIDQ2266074

Jeffrey D. Adams

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/143082

zbMATH Keywords

symplectic groupcoadjoint orbitsdiscrete seriesWeil representationreductive dual pairderived functor bundles

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Analysis on other specific Lie groups (43A80)

Related Items (17)

Discrete decomposability of restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups and its applications ⋮ Unitary highest weight modules ⋮ Coadjoint orbits and reductive dual pairs ⋮ Unnamed Item ⋮ Boundary values of holomorphic functions, singular unitary representations of \(O(p,q)\), and their limits as \(q\to\infty\) ⋮ On Howe's duality theorem ⋮ Unnamed Item ⋮ Singular unitary representations of classical groups ⋮ Lifting of characters on orthogonal and metaplectic groups ⋮ Poincaré series for \(SO(n,1)\) ⋮ Chern-Simons invariants from ensemble averages ⋮ Arithmetic automorphic forms for the nonholomorphic discrete series of \(GSp(2)\) ⋮ On the Discrete Series of Generalized Stiefel Manifolds ⋮ Theta lifting of unitary lowest weight modules and their associated cycles ⋮ Theta lifting for unitary representations with nonzero cohomology ⋮ Geometric realization of discrete series for semisimple symmetric spaces ⋮ 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)

Cites Work

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• On the Segal-Shale-Weil representations and harmonic polynomials
• On some results of Strichartz and of Rallis and Schiffman
• On Eichler's trace formula
• Holomorphic discrete series for the real symplectic group
• Harmonic analysis on hyperboloids
• Transcending Classical Invariant Theory
• Remarks on Classical Invariant Theory
• Weil representation. I. Intertwining distributions and discrete spectrum
• Hamiltonian group actions and dynamical systems of calogero type
• Introduction to Lie Algebras and Representation Theory

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