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Homogeneous Siegel domains

Published online by Cambridge University Press:  22 January 2016

Josef Dorfmeister
Josef Dorfmeister*
Affiliation:
Westfälische Wilhelms-Universität
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In 1935 E. Cartan classified all symmetric bounded domains [6]. At that time he proved that a bounded symmetric domain is homogeneous with respect to its group of holomorphic automorphisms. Thus the more general problem of investigating homogeneous bounded domains arose. It was known to E. Cartan that all homogeneous bounded domains of dimension ≤3 are symmetric [6]. For domains of higher dimension little was known. The first example of a 4-dimensional, homogeneous, non-symmetric bounded domain was provided by I. Piatetsky-Shapiro [41]. In several papers he investigated homogeneous bounded domains [20], [21], [41], [42], [43]. One of the main results is that all such domains have an unbounded realization of a certain type, as a so-called Siegel domain. But many questions still remained open. Amongst them the question for the structure and explicit form of the infinitesimal automorphisms of a homogeneous Siegel domain.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 86 , June 1982 , pp. 39 - 83
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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