HIDDEN SYMMETRIES, SPECTRAL GEOMETRY AND QUATERNIONIC MANIFOLDS

The moduli space of the Calabi-Yau three-folds, which play a role as s uperstring ground states, exhibits the same special geometry that is k nown from nonlinear sigma models in N = 2 supergravity theories. We di scuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional red uction. We analyze the emergence of extra and hidden symmetries. This analysis is then applied to homogeneous special spaces and the implica tions for the classification of homogeneous quaternionic spaces are di scussed.