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