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 149 页 Section 8.5 的商空间、分层与大胞腔定义句
$G$ 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 $B\dot wB$. […] The decomposition of 8.3.8 implies a similar result for the homogeneous space $\mathcal B=G/B$, which is called a flag variety (it is uniquely determined by $G$, up to isomorphism). Let $\pi:G\to\mathcal B$ be the canonical map. Put $X(w)=\pi C(w)$. […] 8.5.1 gives a stratification of $\mathcal B$, i.e. a decomposition of $\mathcal B$ into locally closed pieces called strata. The strata $X(w)$ are affine spaces, called Bruhat cells. […] There is a unique open stratum $X(w_0)$, called the big cell.