Towards a Classification of Homogeneous Tube Domains in C^4

Details Towards a Classification of Homogeneous Tube Domains in C^4 Towards a Classification of Homogeneous Tube Domains in C^4

2004-08-09

arxiv.org/abs/math/0408125v1

Mathematics

Complex Variables

16 pages

Scientific paper

We classify the tube domains in C^4 with affinely homogeneous base whose boundary contains a non-degenerate affinely homogeneous hypersurface. It follows that these domains are holomorphically homogeneous and amongst them there are four new examples of unbounded homogeneous domains (that do not have bounded realisations). These domains lie to either side of a pair of Levi-indefinite hypersurface. Using the geometry of these two hypersurfaces, we find the automorphism groups of the domains.

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