Dual root system
= Dual root system
{title2=$\Phi^\vee$}
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The dual root system of $\Phi$ is $\Phi^\vee=\{\alpha^\vee:\alpha\in\Phi\}$. It has the transposed <Cartan matrix>, so its <Dynkin diagram> reverses every multiple-edge arrow; in particular, $B_n$ and $C_n$ are dual.