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 CP N are constructed. The recurrence relations for a Grassmann manifold G 2,2 are closely studied too.