On quantizing nonnilpotent coadjoint orbits of semisimple Lie groups (Q1868410)

In [Newton, Paul (ed.) et al., Geometry, mechanics, and dynamics. Volume in honor of the 60th birthday of J. E. Marsden. Springer, 523--536 (2002; Zbl 1029.53093)] the author showed that there do not exist polynomial quantizations of the coordinate ring \(P(M)\) of a semisimple coadjoint orbit \(M\subset \text{sl} (2,\mathbb R)^*\). In this paper, the author extends this result to any nonnilpotent coadjoint orbit of a general semisimple Lie group and shows that if \(\mathfrak b\) is a finite-dimensional semisimple Lie algebra and \(M\) is a nonnilpotent coadjoint orbit in \(\mathfrak b^*\), then there are no consistent polynomial quantizations of the coordinate ring \(P(M)\).