On the deformation quantization of coadjoint orbits of semisimple Lie groups

Abstract

In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal enveloping algebra of the Lie algebra of the given Lie group, by a suitable ideal. A comparison with geometric quantization in the case of SU(2) is done where both methods agree.

arXiv comment25 pages, PlainTeX. Some references added

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Quantization of Lie bialgebras, V
• On the Deformation of Time Harmonic Flows

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• The Segre embedding of the quantum conformal superspace
• A review on deformation quantization of coadjoint orbits of semisimple Lie groups
• On the deformation quantization of affine algebraic varieties
• On the Dynamics of the Self Gravitating Ellipsoid in N dimensions and its Deformation Quantization