论文标题
六个vertex模型和杨巴克斯特群的一致性
Integrability of the Six-Vertex model and the Yang-Baxter Groupoid
论文作者
论文摘要
我们研究了六个vertex型号的$ r $ amatrices的杨巴克斯特方程。我们分析了解决方案并提供新的Yang-Baxter方程的新参数化。特别是，我们发现参数化解决方案的最大交换家族概括了来自Aggine量子（Super） - 组的$ r $ amatrices。然后，我们通过非释放含量矩阵的群体固定对杨巴克斯特方程进行了新的参数化。在附录中，我们研究了杨百合机解决方案的一般代数结构，并提出了一种猜想，该猜想扩展了Brubaker，Bump和Friedberg的猜想，即Yang-Baxter溶液上的组成法总是关联的。
We study the Yang-Baxter equation for the $R$-matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized solutions which generalize the $R$-matrices from the affine quantum (super)-groups. Then we give a new parametrization of the Yang-Baxter equation by a groupoid of non-free-fermionic matrices. In the appendix, we study the general algebraic structure of the solutions of the Yang-Baxter and formulate a conjecture that extends the conjecture by Brubaker, Bump, and Friedberg that the composition law on the Yang-Baxter solutions is always associative.
