We construct Zariski-dense surface subgroups in infinitely many commensurability classes of uniform lattices of the split real Lie groups \(\text {SL}(n,\mathbb {R})\) , \(\text {Sp}(2n,\mathbb {R})\) , \(\text {SO}(k+1,k)\) , and \(\text {G}_2\) . These subgroups are images of Hitchin representations. In particular, we show that every uniform lattice of \(\text {Sp}(2n,\mathbb {R})\) , of \(\text {SO}(k+1,k)\) with \(k\equiv 1,2[4]\) and of \(\text {G}_2\) contains infinitely many mapping class group orbits of Zariski-dense Hitchin representations of fixed genus. Together with Long and Thistlethwaite (Exp. Math. 27(1):82–92 2018) and Audibert (2022) it implies that all lattices of \(\text {Sp}(4,\mathbb {R})\) contain a Zariski-dense surface subgroup. This paper follows Audibert (2022), where we constructed Zariski-dense Hitchin representations in non-uniform lattices.
