Anosov triangle reflection groups in SL(3,R)

We identify all Anosov representations of compact hyperbolic triangle reflection groups into $\mathrm{SL}(3,\mathbb R)$. Specifically, we prove that such a representation is Anosov if and only if 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.
Comment: 42 pages, 11 figures