Rational approximation for Hitchin representations

Abstract

We show that for $S$ a closed surface of genus at least $3$, the set of Hitchin representations of ${\pi }_1(S)$ with image in $\mathrm{SL}(n,\mathbf{Q})$ is dense in the Hitchin component. When $n=2$, we recover a particular case of a result of Takeuchi but using a completely different method.