论文标题
扭曲和折叠的Auslander-Reiten颤音以及对量子代数的表示理论的应用
Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras
论文作者
论文摘要
在本文中，我们介绍了类型$ a_ {2n+1} $，$ d_ {n+1} $，$ e_6 $和$ d_4 $的扭曲和折叠的AR-Quivers，与（Triply）扭曲的Coxed Coxeter Elements相关。使用类型$ a_ {2n+1} $和$ d_ {n+1} $的Quivers，我们描述了分母公式和多里（Dorey）的量子代数$ u'_q（b^{（1）} _ {n+1}）$和$ u'_q（c^（c^（1）} _ {1）量子仿射代数。更准确地说，我们可以阅读$ u'_q（b^{（1）} _ {n+1}）$（$ u'_q（c^{（1）} _ {n}）$的分母公式（b^{（1）} _ {n+1}）$（$ u'_q（c^{（1）} _ {n}）$，使用某些折叠的Ar-quiver of type $ a_______的n priover of type $ a_ {2n+1} $ n e n+a {对于$ u'_q（b^{（1）} _ {n+1}）$（resp。U'_q（c^{（1）} _ {n}）$）在扭曲的ar-quiver中应用最小对的概念。通过采用相同的参数，我们提出了$ u'_q（f^{（1）} _ {4}）$和$ u'_q（g^{（1）_ {2}）$的u'_q（f^{（1）_ {4}）$ u'_q（f^{（1）_ {2}）$的猜想分母公式和多里（Dorey）规则。
In this paper, we introduce twisted and folded AR-quivers of type $A_{2n+1}$, $D_{n+1}$, $E_6$ and $D_4$ associated to (triply) twisted Coxeter elements. Using the quivers of type $A_{2n+1}$ and $D_{n+1}$, we describe the denominator formulas and Dorey's rule for quantum affine algebras $U'_q(B^{(1)}_{n+1})$ and $U'_q(C^{(1)}_{n})$, which are important information of representation theory of quantum affine algebras. More precisely, we can read the denominator formulas for $U'_q(B^{(1)}_{n+1})$ (resp. $U'_q(C^{(1)}_{n})$) using certain statistics on any folded AR-quiver of type $A_{2n+1}$ (resp. $D_{n+1}$) and Dorey's rule for $U'_q(B^{(1)}_{n+1})$ (resp. $U'_q(C^{(1)}_{n})$) applying the notion of minimal pairs in a twisted AR-quiver. By adopting the same arguments, we propose the conjectural denominator formulas and Dorey's rule for $U'_q(F^{(1)}_{4})$ and $U'_q(G^{(1)}_{2})$.
