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 provides a tool for the determination of the holomorphic prepotential characterizing the special geometry of these manifolds and necessary in the superconformal tensor calculus of N = 2 supergravity. It is demonstrated 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 characterizing these cosets in N = 2 supergravity theory can be determined from the knowledge of the corresponding embedding, a la Gaillard and Zumino. Our results are used to study some of the duality symmetries of heterotic compactifications of orbifolds with Wilson lines.