Square Integrable Representations and a Plancherel Theorem for Parabolic Subgroups

DOI10.2307/1997753zbMath0395.22008OpenAlexW4253135892MaRDI QIDQ4177784

Frederick W. Keene

Publication date: 1978

Full work available at URL: https://doi.org/10.2307/1997753

zbMATH Keywords

Lie GroupPlancherel FormulaLaplace OperatorLittle GroupIwasawa DecompositionNilpotent GroupReduced Restricted Root System

Mathematics Subject Classification ID

Unitary representations of locally compact groups (22D10) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Nilpotent and solvable Lie groups (22E25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items

A Plancherel Formula for Parabolic Subgroups, Canonical Semi-Invariants and the Plancherel Formula for Parabolic Groups, The Plancherel formula for parabolic subgroups, The Plancherel formula for parabolic subgroups of the classical groups

Cites Work

• Unitary representations of group extensions. I
• Representations of certain semidirect product groups
• The Plancherel formula for parabolic subgroups
• Representations of Semisimple Lie Groups VI: Integrable and Square-Integrable Representations
• 𝐿₂-representations and a Plancherel-type theorem for parabolic subgroups
• The action of a real semisimple Lie group on a complex flag manifold. II. Unitary representations on partially holomorphic cohomology spaces
• Square Integrable Representations of Nilpotent Groups
• Unitary representations of solvable Lie groups
• Harmonic analysis on semisimple Lie groups
• On the existence and irreducibility of certain series of representations
• An extension of Plancherel's formula to separable unimodular groups
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