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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 invo
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