Cusped Borel Anosov representations with positivity

Cusped Borel Anosov representations with positivity

We show that if a cusped Borel Anosov representation from a lattice Γ ⊂ PGL 2 ( R ) to 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 cus...

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Veröffentlicht in:Geometriae dedicata 2024-04, Vol.218 (2), Article 54
Hauptverfasser: Lee, Gye-Seon, Zhang, Tengren
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Representations
Topology
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Zusammenfassung:We show that if a cusped Borel Anosov representation from a lattice Γ ⊂ PGL 2 ( R ) to 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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-024-00895-2