%0 Journal Article
%T Length functions of Hitchin representations
%A Guillaume Dreyer
%J Mathematics
%D 2011
%I arXiv
%R 10.2140/agt.2013.13.3153
%X Given a Hitchin representation $\rho \colon \pi_1(S) \to \PSL_n(\mathbb{R})$, we construct $n$ continuous functions $\ell_i^\rho \colon \mathcal \CH(S) \to \mathbb{R}$ defined on the space of H\"older geodesic currents $\CH(S)$ such that, for a closed, oriented curve $\gamma$ in $S$, the $i$--th eigenvalue of the matrix $\rho(\gamma)\in \PSL_n(\mathbb{R})$ is of the form $\pm \mathrm{exp}\, \ell_i^\rho(\gamma)$: such functions generalize to higher rank Thurston's length function of Fuchsian re\presentations. Identities, diffe\rentiability properties of these lengths $\ell_i^\rho$, as well as applications to eigenvalue estimates, are also considered.
%U http://arxiv.org/abs/1106.6310v3