Canonical Semi-Invariants and the Plancherel Formula for Parabolic Groups

DOI10.2307/1998596zbMath0488.22024OpenAlexW4239212764MaRDI QIDQ3949225

Ronald L. Lipsman, Joseph A. Wolf

Publication date: 1982

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.353.1815

zbMATH Keywords

universal enveloping algebrasemi-invariantparabolic groups

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Other transforms and operators of Fourier type (43A32)

Related Items (14)

Homogeneous hypercomplex structures. I: The compact Lie groups ⋮ A Plancherel Formula for Parabolic Subgroups ⋮ Lie algebraic aspects of the finite nonperiodic Toda flows ⋮ Infinite Kostant cascades and centrally generated primitive ideals of \(U(\mathfrak{n})\) in types \(A_\infty\), \(C_\infty\) ⋮ Commutative polarisations and the Kostant cascade ⋮ Unnamed Item ⋮ Homomorphisms Between Generalized Verma Modules ⋮ Homogeneous hypercomplex structures. II: Coset spaces of compact Lie groups ⋮ Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable Subgroups ⋮ On the Spectra of Quantum Groups ⋮ Centrally generated primitive ideals of \(U(\mathfrak{n})\) in types B and D ⋮ The Capelli identity, tube domains, and the generalized Laplace transform ⋮ Hamiltonian and gradient structures in the Toda flows ⋮ Tempered subgroups and representations with minimal decay of matrix coefficients

Cites Work

• Unnamed Item
• La représentation coadjointe du groupe affine
• The Plancherel formula for parabolic subgroups
• The Plancherel formula for parabolic subgroups of the classical groups
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• Classification and Fourier inversion for parabolic subgroups with square integrable nilradical
• Fourier Inversion on Borel Subgroups of Chevalley Groups: The Symplectic Group Case
• Unitary representations of maximal parabolic subgroups of the classical groups
• Square Integrable Representations and a Plancherel Theorem for Parabolic Subgroups
• Sur les Representations Unitaires des Groupes de Lie Nilpotents. IV
• The action of a real semisimple group on a complex flag manifold. I: Orbit structure and holomorphic arc components
• Unitary representations of solvable Lie groups
• The plancherel formula for group extensions
• Sur les extensions des représentations irréductibles des groupes de Lie nilpotents

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