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) be 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 all such quantizations. We also describe all two parameter U_h(g) invariant quantizations on M, which can be considered as U_h(g) invariant quantizations of the Kirillov-Kostant-Souriau (KKS) Poisson bracket on M. We also consider how those quantizations relate to the natural polarizations of M with respect 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 modules over a quantized function sheaf.