Classification of homogeneous affine tube domains with large automorphism groups in 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 $\frac{(n-2)(n-3)}{2}$.