Most Hitchin representations are strongly dense

TL;DR

This paper proves that most Hitchin representations are strongly dense, meaning any pair of non-commuting elements generate a Zariski-dense subgroup, using algebraic geometry and representation theory techniques.

Contribution

It establishes the strong density of generic Hitchin representations, extending understanding of their algebraic and geometric properties.

Findings

Generic Hitchin representations are strongly dense.

Pairs of non-commuting elements generate Zariski-dense subgroups.

Hitchin representations are Zariski-dense in the representation variety.

Abstract

We prove that generic Hitchin representations are strongly dense: every pair of non commuting elements in their image generate a Zariski-dense subgroup of SL_n(R). The proof uses a theorem of Rapinchuk, Benyash-Krivetz and Chernousov, to show that the set of Hitchin representations is Zariski-dense in the variety of representations of a surface group in SL_n(R).