论文标题
量子仿射代数的图表自动形态和规范基础，II
Diagram automorphisms and canonical bases for quantum affine algebras, II
论文作者
论文摘要
令$ {\ mathbf u} _q^ - $为量子包络代数的负部分，而$σ$ the $ {\ mathbf u} _q^ - $ the代数自动形态是由图自动形态诱导的。令$ \下划线{\ Mathbf U} _q^ - $是从$σ$获得的量子代数，以及$ \ widetilde {\ Mathbf B} $（supp. $ \ \ \ widetilde {\ distiLde {\ undesline {\ mathbf b}} $ pansunical nline {\ mathbf b}} $ pans pans pans pans cultimal carte n usiste。 $ \ usewandline {\ mathbf u} _q^ - $）。假设$ {\ mathbf u} _q^ - $简单地为有限或仿射类型。在我们以前的论文[sz1，2]中，我们已经通过基本方法证明了一个天然的培训$ \ widetilde {\ mathbf b}^σ\ simeq \ simeq \ simeq \ widetilde {\ undesline {\ mathbf B}}} $，在$σ$的情况下。在本文中，我们表明，即使$σ$不可接受，也可能存在这种两次射击。
Let ${\mathbf U}_q^-$ be the negative part of the quantum enveloping algebra, and $σ$ the algebra automorphism on ${\mathbf U}_q^-$ induced from a diagram automorphism. Let $\underline{\mathbf U}_q^-$ be the quantum algebra obtained from $σ$, and $\widetilde{\mathbf B}$ (resp. $\widetilde{\underline{\mathbf B}}$) the canonical signed basis of ${\mathbf U}_q^-$ (resp. $\underline{\mathbf U}_q^-$). Assume that ${\mathbf U}_q^-$ is simply-laced of finite or affine type. In our previous papers [SZ1, 2], we have proved by an elementary method, that there exists a natural bijection $\widetilde{\mathbf B}^σ \simeq \widetilde{\underline{\mathbf B}}$ in the case where $σ$ is admissible. In this paper, we show that such a bijection exists even if $σ$ is not admissible, possibly except some small rank cases.
