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We show that a Hitchin representation is determined by the spectral radii ofthe images of simple, non-separating closed curves. As a consequence, weclassify isometries of the intersection function on Hitchin components ofdimension 3 and on the self-dual Hitchin components in all dimensions. As animportant tool in the proof, we establish a transversality result for positivequadruples of flags.

Simple Length Rigidity for Hitchin Representations