Arithmeticity of discrete subgroups containing horospherical lattices

Abstract

Let $G$ be a semisimple real algebraic Lie group of real rank at least two and $U$ be the unipotent radical of a non-trivial parabolic subgroup. We prove that a discrete Zariski dense subgroup of $G$ that contains an irreducible lattice of $U$ is an arithmetic lattice of $G$. This solves a conjecture of Margulis and extends previous work of Hee Oh.

54 pages

Cited by in corpus (2)

• Hybrid lattices and thin subgroups of Picard modular groups
• Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions