Symplectic Embeddings, the Prepotentials and Automorphic Functions of $\frac{SU(1,n)}{U(1)\otimes SU(n)}$

Abstract

The holomorphic homogeneous prepotential encoding the special geometry of the special Kähler manifolds $\frac{SU(1,n)}{U(1)\otimes SU(n)}$ is constructed using the symplectic embedding of the isometry group $SU(1,n)$ into $Sp(2n+2,\mathbf{R})$. Also the automorphic functions of these manifolds are discussed.

11 pages, TeX, no figures