Spectral decomposition of invariant differential operators on certain nilpotent homogeneous spaces

DOI10.1016/0022-1236(92)90030-MzbMath0784.22003OpenAlexW2075153039MaRDI QIDQ1803320

Frederick P. Greenleaf, Lawrence J. Corwin

Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90030-m

zbMATH Keywords

rational functionsdifferential operatorsmultiplicitiescommutativitycentral decompositionorbit methodsimply connected nilpotent Lie groupmonomial representation

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) 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 (3)

Unnamed Item ⋮ A proof of the polynomial conjecture for nilpotent Lie groups monomial representations ⋮ On the commutativity of the algebra of invariant differential operators on certain nilpotent homogeneous spaces

Cites Work

• Analyse harmonique sur les espaces symétriques nilpotents
• Représentations monomiales des groupes de Lie nilpotents. (Monomial representations of nilpotent Lie groups)
• Résolubilité d'équations différentielles et représentation induites. (Solubility of differential equations and induced representations)
• Abstract Plancherel theorems and a Frobenius reciprocity theorem
• On a connection between nilpotent groups and oscillatory integrals associated to singularities
• On some \(C^ *\)-algebras considered by Glimm
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Sur Les Représentations Unitaires Des Groupes De Lie Nilpotents. III
• Multiplicité un pour les espaces symétriques exponentiels
• On the infinitesimal kernel of irreducible representations of nilpotent Lie groups
• Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups
• A canonical approach to multiplicity formulas for induced and restricted representations of nilpotent lie groups
• Commutativity of invariant differential operators on nilpotent homogeneous spaces with finite multiplicity
• Singular fourier integral operators and representations of nilpotent lie groups
• Orbital Parameters for Induced and Restricted Representations
• Resolution of Singularities and Division of Distributions
• Complex Fourier Analysis on a Nilpotent Lie Group
• Unitary representations of solvable Lie groups
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