A REMARK ON THE N-INVARIANT GEOMETRY OF BOUNDED HOMOGENEOUS DOMAINS

Let $\mathbf {D}$ be a bounded homogeneous domain in ${\mathbb {C}}^n$ . In this note, we give a characterization of the Stein domains in $\mathbf {D}$ which are invariant under a maximal unipotent subgroup N of $Aut(\mathbf {D})$ . We also exhibit an N-invariant potential of the Bergman metric of $...

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Bibliographic Details
Published in:Nagoya mathematical journal 2024-12, Vol.256, p.928-937
Main Authors: GEATTI, LAURA, IANNUZZI, ANDREA
Format: Article
Language:English
Subjects:
Algebra
Decomposition
Invariants
Subgroups
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Summary:Let $\mathbf {D}$ be a bounded homogeneous domain in ${\mathbb {C}}^n$ . In this note, we give a characterization of the Stein domains in $\mathbf {D}$ which are invariant under a maximal unipotent subgroup N of $Aut(\mathbf {D})$ . We also exhibit an N-invariant potential of the Bergman metric of $\mathbf {D}$ , expressed in a Lie theoretical fashion. These results extend the ones previously obtained by the authors in the symmetric case.
ISSN:0027-7630
2152-6842
DOI:10.1017/nmj.2024.12