Coxeter Groups are not higher rank Arithmetic Groups
Group Theory
2014-04-14 v2
Abstract
Let W be an irreducible finitely generated Coxeter group. The geometric representation of W in GL(V) provides a discrete embedding in the orthogonal group of the Tits form (the associated bilinear form of the Coxeter group). If the Tits form of the Coxeter group is non-positive and non-degenerate, the Coxeter group does not contain any finite index subgroup isomorphic to an irreducible lattice in a semisimple group of R-rank greater or equal to 2.
Cite
@article{arxiv.1208.6569,
title = {Coxeter Groups are not higher rank Arithmetic Groups},
author = {Sandip Singh},
journal= {arXiv preprint arXiv:1208.6569},
year = {2014}
}