Normal Siegel Domains

Abstract

In this chapter, we will introduce a special class of homogeneous Siegel domains, the so-called normal Siegel domains. We will first prove that any homogeneous Siegel domain is affinely isomorphic to a normal Siegel domain. Namely, we give a realization of homogeneous Siegel domains by normal Siegel domains. Then we will prove that the classification of normal Siegel domains up to an affine isomorphism is equivalent to the classification of normal matrix sets up to a special unitarily equivalent. Finally, we will give the explicit expression of the Bergman kernel function K$(z,u;\bar z,\bar u)$ on a normal Siegel domain D(V _N ,F) by the transitive affine automorphism group Aff (D(V _N , F)).