HILBERT SPACES OF TENSOR-VALUED HOLOMORPHIC FUNCTIONS ON THE UNIT BALL OF Cn

We study expansion of reproducing kernels for Hilbert spaces of holomorphic functions on the unit ball in Cn with values in the antisymmetric tensor of the tangent and the cotangent spaces. As an application we find the composition series for the analytic continuation of certain families of holo-morphic discrete series. 1. Introduction. The expansion of reproducing kernels of Bergman spaces of holomorphic functions on a domain D in Cn is of considerable interests. If the domain admits an action of a compact group K, then naturally one would like to decompose the space of polynomials into irreducible subspaces of K and ex