量子仿射代数的图自同构和标准基，II
Diagram automorphisms and canonical bases for quantum affine algebras, II
摘要：
设${\mathbf U}_q^-$是量子包络代数的负部分，$σ$是由图自同构导出的${\mathbf U}_q^-$上的代数自同构.设$\underline{\mathbf U}_q^-$是由$σ$得到的量子代数，而$\widetilde{\mathbf B}$（分别为. $\widetilde{\underline{\mathbf B}}$）${\mathbf U}_q^-$的规范有符号基（分别$\underline{\mathbf U}_q^-$）。假设${\mathbf U}_q^-$是有限型或仿射型的单系。在我们以前的文章[SZ]中，我们用初等方法证明了当$σ$是可容许的时，存在自然双射$\widetilde{\mathbf B}^σ \simeq \widetilde{\underline{\mathbf B}}$。在本文中，我们表明，这样的双射存在，即使$σ$是不容许的，可能除了一些小秩的情况下。
英文摘要：
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.
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