Description of unitary representations with highest weight for groups U(p,q)

DOI10.1007/BF01086181zbMath0455.22004MaRDI QIDQ1150051

Grigori Olshanski

Publication date: 1981

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

U(p,q)pseudo-unitary groups

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 (7)

Irreducibility of Certain Universal Holomorphic Harish-Chandra Modules ⋮ IRREDUCIBLE UNITARY REPRESENTATIONS OF SU_p,q I: THE DISCRETE SERIES ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Restriction of representations of \(\mathrm{GL}(n + 1, \mathbb{C})\) to \(\mathrm{GL}(n, \mathbb{C})\) and action of the Lie overalgebra ⋮ Grigori Iosifovich Olshanski ⋮ Weighted Bergman spaces and the holomorphic discrete series of \(\widetilde{U(p,q)}\) ⋮ On Borel–de Siebenthal Representations

Cites Work

• Criteria for the unitarizability of some highest weight modules
• Invariant generalized functions in homogeneous domains
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
• On the Segal-Shale-Weil representations and harmonic polynomials
• Representations of Semisimple Lie Groups IV
• Representations of Semisimple Lie Groups VI: Integrable and Square-Integrable Representations
• The Analytic Continuation of the Discrete Series. II
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• On the Helmholtz resonator
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