TIght maps and holomorphicity

Journal article, 2014

Tight maps were introduced and studied along tight homomorphisms by Burger, Iozzi and Wienhard with aims towards maximal representations. In this paper we show that, with the exception of maps from the Poincaré disc, tight maps into classical Hermitian symmetric spaces must be holomorphic or antiholomorphic. Together with previous results this completely classi_es tight maps into classical codomains.