Class Field Theory
《Class Field Theory》 · 印刷第 204 页 Section 8.3,Definition 8.10 的根系、余根约定及第 219 页 Section 8.7「Integral and Dominant Integral Elements」,Definition 8.36(省略中间内容)
If $(E,R)$ is a root system, then for each root $\alpha\in R$, the coroot $H_\alpha$ is the vector given by $H_\alpha=2\frac{\alpha}{\langle\alpha,\alpha\rangle}$. […] Definition 8.36. Let $\Delta=\{\alpha_1,\ldots,\alpha_r\}$ be a base. Then the fundamental weights (relative to $\Delta$) are the elements $\mu_1,\ldots,\mu_r$ with the property that $2\frac{\langle\mu_j,\alpha_k\rangle}{\langle\alpha_k,\alpha_k\rangle}=\delta_{jk}$, $j,k=1,\ldots,r$.