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 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.