Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 67 页 · Section 13「Abstract theory of weights」章首约定及 Section 13.1「Weights」
Let $\Phi$ be a root system in a euclidean space $E$, with Weyl group $\mathcal W$. […] Let $\Lambda$ be the set of all $\lambda\in E$ for which $\langle\lambda,\alpha\rangle\in\mathbb Z$ ($\alpha\in\Phi$), and call its elements weights. Since $\langle\lambda,\alpha\rangle=\frac{2(\lambda,\alpha)}{(\alpha,\alpha)}$ depends linearly on $\lambda$, $\Lambda$ is a subgroup of $E$ including $\Phi$.