Bruhat order on the Weyl group preserves sending the highest root to a negative root – mathoverflow.net
Ashwin Iyengar
Suppose $G$ is a split connected reductive group over a field $k$ with Weyl group $W$ and root system $\Phi$, with positive roots $\Phi_+$ corresponding to a Borel $B$ with unipotent radical $N$.
If ...