Some Types of Nonsymmetric Homogeneous Domains
Current research in the classification theory of bounded homogeneous domains is mainly concerned with Siegel domains. Pyateckii-Shapiro gave the first example of nonsymmetric bounded homogeneous domains in 1959. Based on that, he introduced the concept of Siegel domains, and proved the following fundamental result : any bounded homogeneous domain is analytically equivalent to an affine homogeneous Siegel domain of the first or second kind. Up to now, the research on Siegel domains has yielded many results. But these works are mainly on the algebraic constructions of automorphism groups of the Siegel domains; the results on properties of geometry and function theory are not numerous.
KeywordsConvex Cone Motion Group Transitive Group Analytic Equivalent Homogeneous Domain
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