Strict quantization of coadjoint orbits.

We obtain a strict quantization of the holomorphic functions on any semisimple coadjoint orbit of a complex semisimple connected Lie group. By restricting this quantization, we also obtain strict star products on a subalgebra of analytic functions for any semisimple coadjoint orbit of a real semisimple connected Lie group. If this Lie group was also compact, the star product is of Wick type. The main tool to construct our quantization is a construction by Alekseev--Lachowska and an explicit formula for the canonical element of the Shapovalov pairing between generalized Verma modules.