Primitive stable representations in higher rank semisimple Lie groups

Abstract

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