On quantizing semisimple basic algebras

Details On quantizing semisimple basic algebras On quantizing semisimple basic algebras

2000-12-18

arxiv.org/abs/math-ph/0012034v2

"Geometry, Mechanics, and Dynamics: Volume in Honor of the 60th Birthday of J.E. Marsden", P. Holmes, P. Newton, & A. Weinstei

Physics

Mathematical Physics

15 pages, Latex2e. Section 3 substantially redone

Scientific paper

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 the coordinate ring of a basic semisimple orbit in sl(2,R)* cannot be consistently polynomially quantized.

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