Hermitian symmetric spaces and their unitary highest weight modules

DOI10.1016/0022-1236(83)90076-9zbMath0517.22014OpenAlexW2017206176MaRDI QIDQ1053127

Hans Plesner Jakobsen

Publication date: 1983

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(83)90076-9

zbMATH Keywords

tensor productsimple Lie algebraHermitian symmetric spaces of noncompact typepositive noncompact rootsunitarizable highest weight modules

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Simple, semisimple, reductive (super)algebras (17B20) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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Cites Work

• Restrictions and expansions of holomorphic representations
• Criteria for the unitarizability of some highest weight modules
• On singular holomorphic representations
• The transfer of invariant pairings to lattices
• The last possible place of unitarity for certain highest weight modules
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• On the Segal-Shale-Weil representations and harmonic polynomials
• The Analytic Continuation of the Discrete Series. II
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