Proper holomorphic maps between bounded symmetric domains revisited (Q471285): Difference between revisions

Inspired by Alexander's classical result, which says that a proper holomorphic self-map of balls in multi-variables must be an automorphism, similar rigidity results have been established for bounded symmetric domains by various authors, such as Henkin and Novikov, Tsai, Tu, etc. In this paper, the authors prove that a proper holomorphic map between two equal-dimensional bounded symmetric domains in multi-variables, one of which being irreducible, must be a biholomorphism. While this result certainly generalizes previously known results, as the authors point out, the focus of the paper is rather on the method of proof, which allows them to avoid relying too heavily on the fine structure of the boundary of bounded symmetric domains. The key ingredients of the proof are Bell's extension theorem, Vigué's Schwarz lemma and Jordan triple systems. The authors also apply a similar argument to prove a similar result for non-symmetric domains with non-compact automorphism groups.