论文标题
四面体和3D反射方程来自量子超级甲虫的nilpotent subergebra的PBW碱基
Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras
论文作者
论文摘要
在本文中，我们研究了等级2和3的所有可能的Dynkin图，与所有可能的Dynkin图相关的量子级超晶体的Nilpotent子代数的过渡矩阵，并检查了与三维（3D）集成性的关系。我们通过A型和3D反射方程获得了Zamolodchikov四面体方程的新解，其中Isaev和Kulish提出了后一个方程，作为Cherednik反射方程的3D类似物。作为我们方法的副产品，Zamolodchikov四面体方程的Bazhanov-Sergeev解决方案被描述为特定A型特定情况的过渡矩阵，它阐明了其代数的起源。我们的工作灵感来自最近连接量子非代数的过渡矩阵与量子坐标环的不可减至表示形式的互换的发展。我们还讨论了过渡矩阵的晶体极限，该矩阵给出了Lusztig lusztig参数化的过渡图的超级类似物。
In this paper, we study transition matrices of PBW bases of the nilpotent subalgebra of quantum superalgebras associated with all possible Dynkin diagrams of type A and B in the case of rank 2 and 3, and examine relationships with three-dimensional (3D) integrability. We obtain new solutions to the Zamolodchikov tetrahedron equation via type A and the 3D reflection equation via type B, where the latter equation was proposed by Isaev and Kulish as a 3D analog of the reflection equation of Cherednik. As a by-product of our approach, the Bazhanov-Sergeev solution to the Zamolodchikov tetrahedron equation is characterized as the transition matrix for a particular case of type A, which clarifies an algebraic origin of it. Our work is inspired by the recent developments connecting transition matrices for quantum non-super algebras with intertwiners of irreducible representations of quantum coordinate rings. We also discuss the crystal limit of transition matrices, which gives a super analog of transition maps of Lusztig's parametrizations of the canonical basis.
