Topology
《Topology》 · 第 253 页 · Chapter 11，Section 11.16
Lusztig started with a lattice $\mathcal{L}$ in $U^+$ over $\mathbb{Z}[q^{-1}]$; he then got a basis of $\mathcal{L}/q^{-1}\mathcal{L}$; these basis elements then have a unique representative in $\mathcal{L}$ that is fixed by $\tau$. These representatives are then a basis of $U^+$ that satisfies the theorem above. Lusztig called this basis the canonical basis of $U^+$. He showed later that it coincides with the basis found by Kashiwara.