Zariski-dense Hitchin representations in uniform lattices

2023/02/20 by Audibert, Jacques
#22E40 #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2302.09837

Abstract

We construct Zariski-dense surface subgroups in infinitely many commensurability classes of uniform lattices of the split real Lie groups SL(n,ℝ), Sp(2n,ℝ), SO(k+1,k), and G₂. These subgroups are images of Hitchin representations. In particular, we show that every uniform lattice of Sp(2n,ℝ), of SO(k+1,k) with k≡1,2[4] and of G₂ contains infinitely many mapping class group orbits of Zariski-dense Hitchin representations of fixed genus. Together with Long-Thistlethwaite and with a previous paper of the author, it implies that all lattices of Sp(4,ℝ) contain a Zariski-dense surface subgroup.

Related

• Zariski-dense surface groups in non-uniform lattices of split real Lie groups
• Most Hitchin representations are strongly dense
• Maximal representations in lattices of the symplectic group
• Zariski dense surface subgroups in SL(n,ℚ) with odd n
• Generic Properties of Hitchin Representations