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Dec 16, 2021 at 8:04 comment added Paul Levy If $C^0$ is the interior of $C$ (i.e. all simple roots $>0$) then we want to show that $wC\neq C$ for all $w\neq 1$ in $W'$. Now find a reduced expression $w=s_{i_1}\ldots s_{i_r}$, then I think the fact that this is a reduced expression for $w$ implies that $\alpha_{i_1}(w(c))<0$ for all $c\in C^0$, or something like that.
Dec 4, 2021 at 11:24 history edited YCor CC BY-SA 4.0
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Dec 4, 2021 at 10:44 history asked fool rabbit CC BY-SA 4.0