Naive Lie Theory
《Naive Lie Theory》 · 印刷第 132 页 Chapter 8 章首及 Section 8.1 的根数据约定、第 135 页 Proposition 8.1.8 前的记号约定及证明中的实空间约定、第 136 页 8.1.11（省略中间内容）
$G$ denotes a connected, reductive, linear algebraic group and $T$ is a maximal torus of $G$. […] Let $(X,R,X^\vee,R^\vee)$ be the root datum of $(G,T)$ (see 7.4.3). […] Let $Q$ ($Q^\vee$) be the subgroup of $X$ ($X^\vee$) spanned by $R$ (respectively: $R^\vee$). […] Introduce a positive definite form $(\ ,\ )$ on $V=\mathbb R\otimes X$ as in 7.1.7. […] Assume that $G$ is semi-simple. […] Put $P=\{x\in V\mid\langle x,R^\vee\rangle\subset\mathbb Z\}$, where $V$ is as before. […] $Q$ is the root lattice of $R$ and $P$ the weight lattice.