Holomorphically induced representations of exponential Lie groups

DOI10.1016/0022-1236(85)90081-3zbMath0581.22011OpenAlexW2085639871MaRDI QIDQ1068214

Richard C. Penney

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90081-3

zbMATH Keywords

polarizationexponential Lie groupKirillov correspondenceexponential Lie algebraholomorphically induced representationPukanszky condition

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Lie algebras of Lie groups (22E60) Solvable, nilpotent (super)algebras (17B30)

Related Items (4)

Harmonically induced representations of solvable Lie groups ⋮ Realization of representations of completely solvable Lie groups in spaces of \(L^ 2\) harmonic forms ⋮ Holomorphically induced representations of some solvable Lie groups ⋮ Semi-invariant vectors associated with holomorphically induced representations of exponential Lie groups

Cites Work

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• Harmonically induced representations of solvable Lie groups
• On the regular representation of a nonunimodular locally compact group
• Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semisimple Lie group
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Lie Cohomology of Representations of Nilpotent Lie Groups and Holomorphically Induced Representations
• On holomorphically induced representations of exponential groups
• Square-Integrable Factor Representations of Locally Compact Groups
• On Induced Representations II: Infinitesimal Induction
• On the Theory of Exponential Groups

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