标题： 量子仿射代数的PBW型凸基底 显示英文标题

标题： Convex Bases of PBW type for Quantum Affine Algebras

摘要： 本文有两个目的。 首先，我们证明在[L,$\S 40.2.5$(a)]中定义的映射对于某些可接受序列是同构。 其次，我们表明该映射为 Drinfel$'$和 Jimbo 的仿射未扭曲量子包络代数$\bup$提供了一种基于庞加莱-伯克霍夫-维特定理（PBW）的凸基。 本文中的计算通过扩展代数的某些外自同构的常规编织群作用得以实现。 显示英文摘要

摘要： This note has two purposes. First we establish that the map defined in [L, $\S 40.2.5$ (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to a convex basis of Poincar\'e--Birkhoff--Witt (PBW) type for $\bup$, an affine untwisted quantized enveloping algebra of Drinfel$'$d and Jimbo. The computations in this paper are made possible by extending the usual braid group action by certain outer automorphisms of the algebra.