Christian Gaetz

Separable elements and Bruhat orders

We prove the curious fact that, in any Coxeter group, the intersection of a principal left weak order ideal $[e,x]_L$ with a principal right weak order ideal $[e,y]_R$ has a unique maximal element $\mathrm{lr}(x,y)$ under Bruhat order. We apply this to resolve a conjecture of Hart and Rowley on involutions in weak orde...