  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.

Geometric Topology;Group Theory;Number Theory