We show that there is a consistent polynomial quantization of the coordinate ring of a basic nilpotent coadjoint orbit of a semisimple Lie group. We also show, at least in the case of a nilpotent orbit in sl(2,R)*, that any such quantization is essentially trivial. Furthermore, we prove that there is no consistent polynomial quantization of the coordinate ring of a basic semisimple orbit in sl(2,R)*.
14 pps. 12/11/00 (Revised 11/14/01) In: Geometry, Dynamics, and Mechanics: Volume in Honor of the 60th Birthday of J.E. Marsden. P. Holmes, P. Newton, & A. Weinstein, Eds., 523536 (Springer, New York, 2002).The followup to this paper is entitled On Quantizing Non-nilpotent Coadjoint Orbits of Semisimple Lie Groups.