[[Root system]]
# Dual root system

Let $\Phi$ be a [[root system]].
To any root $\alpha \in \Phi$ one associated a **coroot** #m/def/geo
$$
\begin{align*}
\alpha^\vee = \frac{2\alpha}{(\alpha,\alpha)}
\end{align*}
$$
and the set of all coroots $\Phi^\vee$ forms the **dual root system**,
whose [[Weyl group]] is canonically isomorphic to that of $\Phi$.[^1972]

  [^1972]: 1972\. [[Sources/@humphreysIntroductionLieAlgebras1972|Introduction to Lie algebras and representation theory]], §9.2, p. 43


> [!missing]- Proof
> #missing/proof


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