SYMMETRY STRUCTURE OF SPECIAL GEOMETRIES

Using techniques from supergravity and dimensional reduction, we study the full isometry algebra of Kahler and quaternionic manifolds with s pecial geometry. These two varieties are related by the so-called c-ma p, which may be understood from dimensional reduction of supergravity theories or by changing chirality assignments in the underlying supers tring theory. An important subclass, studied in detail, consists of th e spaces that follow from real special spaces using the so-called r-ma p. We generally clarify the presence of ''extra'' symmetries emerging from dimensional reduction and give the conditions for the existence o f ''hidden'' symmetries. These symmetries play a major role in our ana lysis. We specify the structure of the homogeneous special manifolds a s coset spaces G/H. These include all homogeneous quaternionic spaces.