Orbital Parameters for Induced and Restricted Representations

DOI10.2307/2001416zbMath0683.22009OpenAlexW4249998014MaRDI QIDQ4732652

Ronald L. Lipsman

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001416

zbMATH Keywords

Lie algebrainductionnilpotent Lie groupsinduced representationfinite measureKirillov theoryconnected Lie groupdirect integral decompositionssimply connected exponential solvable Lie group

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) Induced representations for locally compact groups (22D30)

Related Items (17)

The up-down formula for nil-homogeneous spaces ⋮ Analysis of restrictions of unitary representations of a nilpotent Lie group ⋮ Orbital decompositions of representations of non-simply connected nilpotent groups ⋮ Analysis of some monomial representations of exponential solvable Lie groups ⋮ Visible actions and criteria for multiplicity-freeness of representations of Heisenberg groups ⋮ The moment map for a multiplicity free action ⋮ A proof of the polynomial conjecture for nilpotent Lie groups monomial representations ⋮ Sur les restrictions des représentations unitaires des groupes de Lie résolubles exponentiels. (On the restrictions of unitary representations of exponential solvable Lie groups) ⋮ The multiplicity function of mixed representations on completely solvable Lie groups ⋮ On the commutativity of the algebra of invariant differential operators on certain nilpotent homogeneous spaces ⋮ Entrelacement des restrictions des représentations unitaires des groupes de Lie nilpotents. (Intertwining of restriction of unitary representations of nilpotent Lie groups) ⋮ The Structure of the Space of Coadjoint Orbits of an Exponential Solvable Lie Group ⋮ Spectral decomposition of invariant differential operators on certain nilpotent homogeneous spaces ⋮ Decomposition of quasi-regular representations induced from discrete subgroups of nilpotent Lie groups ⋮ The Penney-Fujiwara Plancherel formula for Gelfand pairs ⋮ The orbit method and Gelfand pairs, associated with nilpotent Lie groups ⋮ Unnamed Item

Cites Work

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• Théorie de Mackey pour les groupes de Lie algébriques
• Harmonic analysis on non-semisimple symmetric spaces
• Orbit theory and harmonic analysis on Lie groups with co-compact nilradical
• Orbit theory and representations of Lie groups with co-compact radical
• Characters of Lie groups. II: Real polarizations and the orbital-integral character formula
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Harmonic induction on Lie groups.
• Solvability of invariant differential operators with variable coefficients
• Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups
• Complex Algebraic Geometry and Calculation of Multiplicities for Induced Representations of Nilpotent Lie Groups
• A canonical approach to multiplicity formulas for induced and restricted representations of nilpotent lie groups
• Unitary Representations of Lie Groups with Cocompact Radical and Applications
• Harmonic Analysis on Grassmannian Bundles
• Singular Points of Complex Hypersurfaces. (AM-61)
• Étude de certaines représentations induites d'un groupe de Lie résoluble exponentiel
• The plancherel formula for group extensions
• Sur les extensions des représentations irréductibles des groupes de Lie nilpotents

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