Cusped Borel Anosov representations with positivity

Abstract

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.

13 pages