Generic Properties of Hitchin Representations

Let G be a split real form of a complex simple adjoint group and let S be a closed orientable surface of genus at least 2. We show that for generic PSL₂ₖ₋₁(R)-Hitchin representations ρ, the middle eigenvalue of ρ(x) is not equal to 1 for all non-trivial elements x∈ π₁(S). Using the same technique, we prove that the set of strongly dense G-Hitchin representations is generic. This generalizes the result of Long, Reid and Wolff for the G=PSLₙ(R) case.