Classification of homogeneous affine tube domains with large automorphism groups in arbitrary dimensions

TL;DR

This paper classifies certain complex tube domains in arbitrary dimensions based on the homogeneity of their boundary and the nature of their Levi form, expanding understanding of their automorphism groups.

Contribution

It provides a comprehensive classification of affine homogeneous tube domains with specific Levi form conditions in any dimension.

Findings

Classified tube domains with positive definite Levi form.

Classified tube domains with Lorentzian Levi form and large affine isotropy.

Extended classification results to arbitrary dimensions.

Abstract

We classify tube domains in $\mathbb C^{n+1}$ ($n\ge 1$) with affinely homogeneous base of their boundary and a.) with positive definite Levi form and b.) with Lorentzian type Levi form and affine isotropy of dimension at least $\frac{(n-2)(n-3)}2$.