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Strict deformation quantization on a pseudo-Kähler orbit of a compact Lie group. (English. Russian original) Zbl 0932.37071
Funct. Anal. Appl. 32, No. 1, 51-53 (1998); translation from Funkts. Anal. Prilozh. 32, No. 1, 66-68 (1998).
Results of previous works are used to construct a strict deformation quantization on an orbit of a compact semisimple Lie group for the case the orbit is endowed with a given invariant pseudo-Kähler polarization. Deformation quantization on arbitrary Kähler manifolds is generalized to pseudo-Kähler manifolds.

MSC:
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
81S10 Geometry and quantization, symplectic methods
53D50 Geometric quantization
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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References:
[1] A. Weinstein, Astérisque,227, 389–409 (1995).
[2] A. V. Karabegov, Trans. Amer. Math. Soc. (1998), to appear.
[3] F. Bayen et al., Ann. Phys.,111, No. 1, 1–151 (1978). · doi:10.1016/0003-4916(78)90221-X
[4] A. V. Karabegov, Funkts. Anal. Prilozhen.,30, No. 2, 87–89 (1996).
[5] F. A. Berezin, Izv. Akad. Nauk SSSR, Ser. Mat.,38, 1116–1175 (1974).
[6] M. Cahen, S. Gutt, and J. H. Rawnsley, Trans. Amer. Math. Soc.,337, No. 1, 73–98 (1993). · Zbl 0788.53062 · doi:10.2307/2154310
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