Vol. 271, No. 1, 2014

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Proper holomorphic maps between bounded symmetric domains revisited

Gautam Bharali and Jaikrishnan Janardhanan

Vol. 271 (2014), No. 1, 1–24
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
Authors
Gautam Bharali
Department of Mathematics
Indian Institute of Science
Bangalore 560012
India
Jaikrishnan Janardhanan
Department of Mathematics
Indian Institute of Science
Bangalore 560012
India