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$\begingroup$ And note that the polynomial $\Delta:=\prod_{i<j } (x_i - x_j)$ is positive on the $A_n$ chambers and negative on the non-$A_n$ chambers. This polynomial is very motivated in this context; it is the minimal polynomial (up to sign) which vanishes on all the hyperplanes. $\endgroup$

David E Speyer
– David E Speyer

2022-03-17 15:45:30 +00:00
Commented Mar 17, 2022 at 15:45

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