On quantizing semisimple basic algebras

2000/12/31 by Mark J. Gotay
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.SG

paper · pdf

published as "Geometry, Mechanics, and Dynamics: Volume in Honor of the 60th Birthday of J.E. Marsden", P. Holmes, P. Newton, & A. Weinstein, Eds., 523--536 (Springer, New York, 2002). · 15 pages, Latex2e. Section 3 substantially redone

arxiv created 2001/11/15 · arxiv updated 2009/11/30

Abstract

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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