On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I

DOI10.1007/BF01456843zbMath0629.22004WikidataQ115393471 ScholiaQ115393471MaRDI QIDQ1093748

Niels Vigand Pedersen

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164443

zbMATH Keywords

coadjoint orbitdifferential operatorsWeyl quantizationsymplectic manifoldreal polarizationhomogeneous line bundlecanonical symplectic formintegral orbitsquantizable functions

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (17)

Covariant deformations on polarized orbits of a Lie group ⋮ Covariant star-products ⋮ Geometric Quantization and The Universal Enveloping Algebra of a Nilpotent Lie Group ⋮ Beyond the classical Weyl and Colin de Verdière's formulas for Schrödinger operators with polynomial magnetic and electric fields ⋮ Homogeneous star products and closed integral formulas ⋮ Canonical coordinates for a class of solvable groups ⋮ Coadjoint orbits in duals of Lie algebras with admissible ideals ⋮ Semisimple coadjoint orbits and cotangent bundles ⋮ The behavior of Fourier transforms for nilpotent Lie groups ⋮ The geometric nature of the Flaschka transformation ⋮ Modulation spaces of symbols for representations of nilpotent Lie groups ⋮ Polarized deformations of algebras on the coadjoint orbits of exponential groups ⋮ Coadjoint orbits and characteristic varieties. ⋮ Lie aspects of the dynamics of self-gravitating ellipsoids in n dimensions ⋮ A deformation approach of the Kirillov map for exponential groups ⋮ Construction of canonical coordinates for exponential Lie groups ⋮ Orbits and primitive ideals of solvable Lie algebras

Cites Work

• Unnamed Item
• Method of orbits in the representation theory of complex Lie groups
• Lectures on geometric quantization
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Covariance and geometrical invariance in *quantization
• On the Theory of Exponential Groups
• La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente

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