Uh(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 Uh(g) be a quantum group corresponding to G. We construct a universal family of Uh(g) invariant quantizations of the sheaf of functions on M and describe all such quantizations. We also describe all two parameter Uh(g) invariant quantizations on M , which can be considered as Uh(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 oneand two-sided Uh(g) invariant modules over a quantized function sheaf.