Quantitative properties of convex representations

Letbe a discrete subgroup of PGL.d; R/. Fix a norm kk on R d and letN .t/ be the number of elements inwhose operator norm ist. In this article we prove an asymptotic for the growth ofN .t/ whent !1 for a class of 's which contains, in particular, Hitchin representations of surface groups and groups dividing a convex set of P.R d /. We also prove analogue counting theorems for the growth of the spectral radii. More precise information is given for Hitchin representations.