Title: Simple Length Rigidity for Hitchin Representations,
Abstract: We show that a Hitchin representation is determined by the spectral radii of
the images of simple, non-separating closed curves. As a consequence, we
classify isometries of the intersection function on Hitchin components of
dimension 3 and on the self-dual Hitchin components in all dimensions. As an
important tool in the proof, we establish a transversality result for positive
quadruples of flags.