Proper holomorphic mappings between generalized pseudoellipsoids (Q1175924)

Given a vector \(\alpha=(\alpha_ 1,\ldots,\alpha_ n)\in({\mathbb{R}}^ +)^ n\), consider a generalized pseudoellipsoid \(\sum(\alpha)=\{z\in{\mathbb{C}}^ n: \sum^ n_{j=1}| z_ j|^{2\alpha_ j}<1\}\). The authors study proper holomorphic mappings between \(\sum(\alpha)\) and \(\sum(\beta)\). They show that such a mapping exists iff, after a permutation, \(\alpha=\lambda\beta\) with \(\lambda\in{\mathbb{N}}\). They also give conditions under which such a mapping may be factorized by automorphisms of \(\sum(\alpha)\).