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A torus subgroup of the isotropy group of a bounded homogeneous domain - MaRDI portal

A torus subgroup of the isotropy group of a bounded homogeneous domain (Q1034708)

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scientific article; zbMATH DE number 5627043
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A torus subgroup of the isotropy group of a bounded homogeneous domain
scientific article; zbMATH DE number 5627043

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    A torus subgroup of the isotropy group of a bounded homogeneous domain (English)
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    6 November 2009
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    According to the main result which answers a question posed by \textit{A. Hundemer} [Manuscr. Math. 98, No.~4, 403--408 (1999; Zbl 0935.32018)] in the negative, given a bounded homogeneous domain in a finite dimensional complex vector space, the isotropy subgroup of any point in the holomorphic automorphism group admits a non-trivial torus subgroup. The proof is based on the standard Siegel domain realization of homogeneous domains and provides specific constructions for both the cases of tube-, respectively, non-tube type domains.
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    holomorphic automorphism group
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    isotropy group
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    bounded homogeneous domain
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    Siegel domain
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    tube domain
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