A collar lemma for partially hyperconvex surface group representations

We show that a collar lemma holds for Anosov representations of fundamental groups surfaces into S L ( n , R stretchy="false">) SL(n,\mathbb {R}) satisfy partial hyperconvexity properties inspired from Labourie’s work. This is the case several open sets not contained in higher rank Teichmüller spaces, as well alttext="normal Theta"> mathvariant="normal">Θ encoding="application/x-tex">\Theta -positive O p q O p q encoding="application/x-tex">SO(p,q) if alttext="p greater-than-or-equal-to 4"> ≥ 4 encoding="application/x-tex">p\geq 4 . moreover ‘positivity properties’ known Hitchin representations, such being positively ratioed and having positive eigenvalue ratios, also hold partially hyperconvex representations.