  In this paper we consider the problem of deformation quantization of the
algebra of polynomial functions on coadjoint orbits of semisimple lie groups.
The deformation of an orbit is realized by taking the quotient of the universal
enveloping algebra of the Lie algebra of the given Lie group, by a suitable
ideal. A comparison with geometric quantization in the case of SU(2) is done
where both methods agree.
