RELATIONS BETWEEN THE AUTOMORPHISM GROUPS FOR BOUNDED SYMMETRIC DOMAINS AND ORDERED SYMMETRIC SPACES

摘要

We will consider the relation between the holomorphic automorphism group of an irreducible bounded symmetric domain of tube type and the automorphism group of the ordered structure of a symmetric space of Cayley type. A bounded symmetric domain is said to be of tube type, if it is realized as a tube domain over a homogeneous selfdual open convex cone. A symmetric space of Cayley type is a pseudo-Riemannian symmetric space which is a higher-dimensional version of the one-sheeted hyperboloid H in R~3. H has the natural ordered structure formed by the two rulings.