Regularization of the Covariant Derivative on Curved Space by Finite Matrices

In a previous paper [M.~Hanada, H.~Kawai and Y.~Kimura, Prog. Theor. Phys.114 (2005), 1295] it is shown that a covariant derivative on any n-dimensionalRiemannian manifold can be expressed in terms of a set of n matrices, and a newinterpretation of IIB matrix model, in which the diffeomorphism, the localLorentz symmetry and their higher spin analogues are embedded in the unitarysymmetry, is proposed. In this article we investigate several coset manifoldsin this formulation and show that on these backgrounds, it is possible to carryout calculations at the level of finite matrices by using the properties of theLie algebras. We show how the local fields and the symmetries are embedded ascomponents of matrices and how to extract the physical degrees of freedomsatisfying the constraint proposed in the previous paper.Comment: 21pages, no figure, to appear in Prog. Theor. Phy