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