Abstract
In this note we show the marked length rigidity of symmetric spaces. More precisely, if X and Y are symmetric spaces of noncompact type without Euclidean de Rham factor, with G 1 and G 2 corresponding real semisimple Lie groups, and Γ 1⊂ G 1, Γ 2⊂ G 2 are Zariski dense subgroups with the same marked length spectrum, then X= Y and Γ 1, Γ 2 are conjugate by an isometry. As an application, we answer in the affirmative a Margulis's question and show that the cross-ratio on the limit set determines the Zariski dense subgroups up to conjugacy. We also embed the space of nonparabolic representations from Γ to G into R Γ .
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