2 problems

Let $\Delta$ be a simply-laced root system with highest root $\theta$, and let $\theta$ be fundamental. For a simple root $\alpha$, let $\EuScript F_{\alpha}$ be the associated min…

Let $(W,S)$ be a Coxeter system with root system $cPhi$, positive roots $cPhi^+$, and inversion set $N(w)$ for $w eqthinspacecin W$. A positive root $a eqthinspacecincPhi^+$ is sma…