SYMPLECTIC EMBEDDINGS AND SPECIAL KAHLER GEOMETRY OF CP(N-1,1)

The embedding of the isometry group of the coset spaces SU(1,n)/[U(I) x SU(n)] in Sp (2n + 2, R) is discussed. Knowledge of such embedding p rovides a tool for the determination of the holomorphic prepotential c haracterizing the special geometry of these manifolds and necessary in the superconformal tensor calculus of N = 2 supergravity. It is demon strated that there exist certain embeddings for which the homogeneous prepotential does not exist. Whether a holomorphic function exists or not, the dependence of the gauge kinetic terms on the scalars characte rizing these cosets in N = 2 supergravity theory can be determined fro m the knowledge of the corresponding embedding, a la Gaillard and Zumi no. Our results are used to study some of the duality symmetries of he terotic compactifications of orbifolds with Wilson lines.