Noncommutative Deformations of Locally Symmetric Kähler manifolds

Abstract

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric Kähler manifold. This quantization method is one of the ways to perform a deformation quantization of Kähler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric Kähler manifolds and $\mathbb{C}{P}^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.

25pages. Typos in Theorem 3.5, Proposition 4.1, and so on are corrected