Anosov triangle reflection groups in SL(3,R)

Abstract

We identify all Anosov representations of compact hyperbolic triangle reflection groups into the higher rank Lie group $\mathrm{SL}(3,\mathbb R)$. Specifically, we prove that such a representation is Anosov if and only if either it lies in the Hitchin component of the representation space, or it lies in the "Barbot component" and the product of the three generators of the triangle group has distinct real eigenvalues. Unlike representations in the Hitchin component, Anosov representations in the Barbot component have non-convex boundary maps.