Holomorphically induced representations of some solvable Lie groups

DOI10.1006/jfan.2001.3793zbMath0995.22001OpenAlexW1978659908MaRDI QIDQ5955069

Junko Inoue

Publication date: 17 October 2002

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

Full work available at URL: https://doi.org/10.1006/jfan.2001.3793

zbMATH Keywords

coadjoint orbitsnilpotent Lie groups\(j\)-algebraholomorphically induced representationsorbit methodweak polarization

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25)

Related Items (2)

\(C^\ast\)-dynamical systems of solvable Lie groups ⋮ Semi-invariant vectors associated with holomorphically induced representations of exponential Lie groups

Cites Work

• Holomorphically induced representations of exponential Lie groups
• Harmonically induced representations of solvable Lie groups
• Abstract Plancherel theorems and a Frobenius reciprocity theorem
• Nontriviality of the space of holomorphically induced representations of a solvable Lie 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
• Uniform convergence and decay of Fourier series on compact nilmanifolds
• Étude de certaines représentations induites d'un groupe de Lie résoluble exponentiel
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