Let be a semisimple real algebraic Lie group of real rank at least , and let be the unipotent radical of a nontrivial parabolic subgroup. We prove that a discrete Zariski-dense subgroup of that contains an irreducible lattice of is an arithmetic lattice of . This solves a conjecture of Margulis and extends previous works of Selberg and Oh.
"Arithmeticity of discrete subgroups containing horospherical lattices." Duke Math. J. 169 (8) 1485 - 1539, 1 June 2020. https://doi.org/10.1215/00127094-2019-0082