Proper holomorphic mappings between symmetrized ellipsoids

Abstract

We characterize the existence of proper holomorphic mappings in the special class of bounded $(1,2,...,n)$-balanced domains in ${\mathbb{C}}^n$, called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groupof these domains.

10 pages, some modifications