Algebraic and differential star products on regular orbits of compact Lie groups

In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are re-strictions of deformations on the dual of the Lie algebra. We prove that there are non isomorphic deformations in the fam-ily. The star products are not differential, unlike the star products considered in other approaches. We make a com-parison with the differential star product canonically defined by Kontsevich’s map. 1. Introduction. Coadjoint orbits of Lie groups are symplectic manifolds that can be used to model physical systems that have a continuous group of symmetries. The Kirillov-Kostant orbit principle allows in many cases to associate canonically a unitary representation to the orbit. The Hilbert space of the representa