U-h(g) invariant quantization of coadjoint orbits and vector bundles over them

Let M be a coadjoint semisimple orbit of a simple Lie group G. Let U-h(g) b e a quantum group corresponding to G. We construct a universal family of U- h(g) invariant quantizations of the sheaf of functions on M and describe al l such quantizations. We also describe all two parameter U-h(g) invariant q uantizations on M, which can be considered as U-h(g) invariant quantization s of the Kirillov-Kostant-Souriau (KKS) Poisson bracket on M. We also consi der how those quantizations relate to the natural polarizations of M with r espect to the KKS bracket. Using polarizations, we quantize the sheaves of sections of vector bundles on M as one- and two-sided U-h(g) invariant modu les over a quantized function sheaf. (C) 2001 Elsevier Science B.V. All rig hts reserved.