Naive Lie Theory
《Naive Lie Theory》 · 印刷第 132、137 页的群、Weyl 群与 Borel 子群约定；第 144 页双陪集记号；第 150 页 8.5.4 的闭包偏序定义；第 153 页 Notes 的 Bruhat order 命名句
$G$ denotes a connected, reductive, linear algebraic group and $T$ is a maximal torus of $G$. […] Let $W=N_G(T)/T$ be the Weyl group of $(G,T)$ (see 7.1.4). […] Let $B$ be a Borel subgroup of $G$ containing $T$. […] Let $(\dot w)_{w\in W}$ be a set of representatives in $N_G(T)$ of the elements of $W$. We denote by $C(w)$ the double coset $B\dot wB$. […] Let $w\in W$. It follows from 2.3.3 (i) that the closure $\overline{C(w)}$ is a union of some $C(x)$. We define an order relation on $W$ by $x\le w$ if $C(x)\subset\overline{C(w)}$ (it is immediate that this relation defines an ordering). […] The order on $W$ of 8.5.4 is sometimes called the Bruhat order, but it was first introduced by Chevalley.