We show that if a cusped Borel Anosov representation from a lattice $\Gamma \subset \mathsf{ PGL}_2(\mathbb{ R})$ to $\mathsf{ PGL}_d(\mathbb{ R})$ contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov representation that is not Hitchin is never cusped Borel Anosov.
Categories: math.DG math.GR