Let be a discrete subgroup of . Fix a norm on and let be the number of elements in whose operator norm is . In this article we prove an asymptotic for the growth of when for a class of ’s which contains, in particular, Hitchin representations of surface groups and groups dividing a convex set of . We also prove analogue counting theorems for the growth of the spectral radii. More precise information is given for Hitchin representations.
Cite this article
Andrés Sambarino, Quantitative properties of convex representations. Comment. Math. Helv. 89 (2014), no. 2, pp. 443–488DOI 10.4171/CMH/324