Cayley Transforms and Symmetry Conditions for Homogeneous Siegel Domains

Abstract

In this article we first present a family of Cayley transforms of a homogeneous Siegel domain. We then give characterizations of symmetric Siegel domains among homogeneous Siegel domains in terms of norm equalities involving the Cayley transforms. Applications of these characterizations to analysis on Siegel domains (the Berezin transforms and the Poisson kernel) are also exhibited.