A review on deformation quantization of coadjoint orbits of semisimple Lie groups

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In this paper we make a review of the results obtained in previous works by the authors on deformation quantization of coadjoint orbits of semisimple Lie groups. We motivate the problem with a new point of view of the well known Moyal-Weyl deformation quantization. We consider only semisimple orbits. Algebraic and differential deformations are compared.
Summary of the talks presented at "Rencontres Mathematiques de Glanon" (Glanon) (2001) (to appear in the Proceedings of the conference) and "XXVIII Reunion Bienal de la RSEF, Jornadas de Fisica Teorica", Sevilla, (2001). AMS-LaTeX, 15 pages

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