Thin right‐angled Coxeter groups in some uniform arithmetic lattices

Abstract

Using a variant of an unpublished argument due to Agol, we show that an irreducible right-angled Coxeter group on n ⩾ 3 ${n \geqslant 3}$ vertices embeds as a thin subgroup of a uniform arithmetic lattice in an indefinite orthogonal group O ( p , q ) $\mathrm{O}(p, q)$ for some p , q ⩾ 1 $p, q \geqslant 1$ satisfying p + q = n $p+q=n$ .