Remark on proper holomorphic maps between reducible bounded symmetric domains
The author studies proper holomorphic maps \(f:\Omega \to \omega \) between two bounded symmetric domains when the source domain \(\Omega \) is not irreducible. If \(\Omega \times \cdots \times \Omega _k\) is the decomposition of the domain \(\Omega \) into a product of irreducible domains, and similarly \(\omega =\omega _1 \times \cdots \times \omega _k\) is the decomposition of \(\omega \), one says that a proper map \(f:\Omega \to \omega \) is a product map if \(f=(f_1,\ldots ,f_k)\) where \(f_j:\Omega _j\to \omega _j\) is a proper holomorphic map, up to permutation. One of the main results of the paper states that a proper holomorphic map between two bounded symmetric domains with the same dimension is a product map. The proof involves the geometry of the boundary components of an irreducible bounded symmetric domain. The irreducibility of the generic norm of an irreducible bounded symmetric domain is used to prove the product property.
scientific article; zbMATH DE number 6965373
scientific article