Proper affine actions for right-angled Coxeter groups

Jeffrey Danciger, François Guéritaud, Fanny Kassel

For any right-angled Coxeter group $\Gamma$ on $k$ generators, we construct proper actions of $\Gamma$ on $\mathrm{O}(p,q+1)$ by right and left multiplication, and on the Lie algebra $\mathf…