Finite step Rigidity of Hitchin representations and special Margulis-Smilga spacetimes

Abstract

In this article we use the "escape from subvarieties lemma" introduced by Eskin-Mozes-Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a similar finite step rigidity result for the Cartan spectra of representations of a finitely generated group inside a connected semisimple real algebraic Lie group with trivial center.

Hitchin representations of Fuchsian groups

“…It would be interesting to know whether or not finitely many curves suffice. (Sourav Ghosh [46] recently showed that there are finitely many elements of π 1 (S) whose full Jordan projections determine a point in H d (S). )…”