Quantization of Kähler manifolds. II. (English) Zbl 0788.53062

Cahen, Michel; Gutt, Simone; Rawnsley, John

Trans. Am. Math. Soc. 337, No. 1, 73-98 (1993).

Summary: [Part I, cf. J. Geom. Phys. 7, No. 1, 45-62 (1990; Zbl 0719.53044).]
We use Berezin’s dequantization procedure to define a formal \(*\)-product on a dense subalgebra of the algebra of smooth functions on a compact homogeneous Kähler manifold \(M\). We prove that this formal \(*\)-product is convergent when \(M\) is a Hermitian symmetric space.

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
53D50	Geometric quantization

Keywords:

Berezin’s dequantization; homogeneous Kähler manifold; formal \(*\)- product; hermitian symmetric space

Citations:

Zbl 0719.53044