English

The orbital counting problem for hyperconvex representations

Group Theory 2014-07-15 v2 Dynamical Systems

Abstract

We give a precise counting result on the symmetric space of a noncompact real algebraic semisimple group G,G, for a class of discrete subgroups of GG that contains, for example, representations of a surface group on PSL(2,R)×PSL(2,R),\textrm{PSL}(2,\mathbb R)\times\textrm{PSL}(2,\mathbb R), induced by choosing two points on the Teichm\"uller space of the surface; and representations on the Hitchin component of PSL(d,R).\textrm{PSL}(d,\mathbb R). We also prove a mixing property for the Weyl chamber flow in this setting.

Keywords

Cite

@article{arxiv.1203.0280,
  title  = {The orbital counting problem for hyperconvex representations},
  author = {Andres Sambarino},
  journal= {arXiv preprint arXiv:1203.0280},
  year   = {2014}
}
R2 v1 2026-06-21T20:27:46.179Z