On the occurrence of admissible representations in the real Howe correspondence in stable range

DOI10.1007/s00229-007-0161-8zbMath1145.22006OpenAlexW2037543619MaRDI QIDQ930578

Tomasz Przebinda, Victor Protsak

Publication date: 1 July 2008

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-007-0161-8

zbMATH Keywords

oscillator representationstable rangereductive dual pairsmixed modelHowe correspondence

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (6)

The explicit theta correspondence for reductive dual pairs \((\mathrm{Sp}(p,q),O^{\ast}(4))\) ⋮ Explicit induction principle and symplectic-orthogonal theta lifts ⋮ Invariants and -spectrums of local theta lifts ⋮ Parity preservation of $K$-types under theta correspondence ⋮ Local theta lifting of generalized Whittaker models associated to nilpotent orbits ⋮ Conservation relations for local theta correspondence

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 explicit duality correspondence of (\(\text{Sp}(p,q),\text{O}^{*}(2n)\))
• Reductive dual pair correspondence for complex groups
• Local geometry of orbits for an ordinary classical Lie supergroup
• On the Howe correspondence for symplectic-orthogonal dual pairs
• Transcending Classical Invariant Theory

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