Geometric limit sets of higher rank lattices

Abstract

Let $G$ be a semisimple Lie group of $\mathbb{R}$-rank at least 2 and $\varGamma$ a discrete subgroup of $G$. We consider the limit set of $\varGamma$ in the geometric boundary of the symmetric space associated with $G$. We define the notion of conical and horospherical limit points. In the case of irreducible non-uniform lattices, by using the two Tits building structures, we distinguish the location of their conical limit points. The limit sets of generalized Schottky groups contained in Hilbert modular groups are studied.