Maximal representations in lattices of the symplectic group
arXiv:2307.06791
Abstract
We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k.
17 pages, comments are welcome