Higher Pappus-Schwartz representations

R. Schwartz recently revisited a construction of a family of representations of the modular group into PGL(3,R), proving that it parametrizes the boundary of a certain connected component of representations consisting of Anosov representations. We use a generalized version of Pappus's hexagon theorem to define a higher dimensional analog of this family. We prove that in dimension 3 these representations are "extended geometrically finite", a notion of relative Anosov representation introduced by T. Weisman. This is joint work in progress with W. Dimoune.