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Abstract We show that if a cusped Borel Anosov representation from a lattice PGL₂ ({\, {R\, }}) Γ ⊂ PGL 2 (R) to PGLd ({\, {R\, }}) PGL d (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.
Lee et al. (Wed,) studied this question.
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