Proper holomorphic maps between bounded symmetric domains revisited

Gautam Bharali and Jaikrishnan Janardhanan

Vol. 271 (2014), No. 1, 1–24

DOI: 10.2140/pjm.2014.271.1

Abstract

We prove that a proper holomorphic map between two nonplanar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.

Keywords

bounded symmetric domains, Harish-Chandra realization, Jordan triple systems, proper holomorphic maps, rigidity, Schwarz lemma

Mathematical Subject Classification 2010

Primary: 32H02, 32M15

Secondary: 32H40

Milestones

Received: 10 June 2013

Accepted: 19 December 2013

Published: 10 September 2014