On the automorphisms of Siegel domains (Q1917960)

This paper studies strongly pseudoconvex Siegel domain \(D_F\subseteq \mathbb{C}^n\oplus \mathbb{C}^m\) with the edge manifold \(M_F\) and its associated convex cone \(\Gamma_F\subseteq \mathbb{R}^m\), à la Piatetskii-Shapiro. Two results about the automorphisms of \(D_F\) are proved. The first asserts that if \(D_F\) has a holomorphic automorphism \(\Psi\) which extends holomorphically to a neighbourhood of the edge \(M_F\), then \(\Psi\) is an affine automorphism. The second presents a sufficient condition for \(D_F\) to be \(\mathbb{C}\)-linearly equivalent to a product of a Heisenberg ball and a strongly pseudoconvex Siegel domain of lower dimension.