Primitive stable representations in higher rank semisimple Lie groups

We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $Σ$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the $σ_{mod}$-regularity for convex projective structures and positive representations. Then we show that the holonomies of convex projective structures and positive representations on $Σ$ are all primitive stable if $Σ$ has one boundary component.

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