Realization of representations of completely solvable Lie groups in spaces of \(L^ 2\) harmonic forms

DOI10.1016/0022-1236(91)90017-YzbMath0724.22008OpenAlexW2077588633MaRDI QIDQ2644779

Richard C. Penney

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1016/0022-1236(91)90017-y

zbMATH Keywords

irreducible representationLie algebracomplex line bundleharmonic spacesharmonic formssolvable Lie groupssemi-invariant measurecoadjoint G-orbitKirillov mappingspace of (0,p) forms

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Nilpotent and solvable Lie groups (22E25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Cites Work

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• Holomorphically induced representations of exponential Lie groups
• Harmonically induced representations of solvable Lie groups
• The structure of rational homogeneous domains in \({\mathbb{C}}^ n\)
• The Mautner phenomenon for general unitary representations
• 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
• Sur La Forme Hermitienne Canonique Des Espaces Homogenes Complexes
• Realization of Square-Integrable Representations of Unimodular Lie Groups on L 2 -Cohomology Spaces
• Lie Cohomology of Representations of Nilpotent Lie Groups and Holomorphically Induced Representations
• On holomorphically induced representations of exponential groups
• On the Theory of Exponential Groups
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)

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