THE REPRESENTATIVE DOMAIN OF A HOMOGENEOUS BOUNDED DOMAIN

Abstract

The representative domain gives a nice realization for a homogeneous bounded domain, which is a generalization of the Harish-Chandra realization for a symmetric bounded domain. We show that the representative domain coincides with the image of the Cayley transform introduced by Penney and Nomura. As an application, we see that a homogeneous bounded domain is symmetric if and only if its representative domain is convex.