论文标题
解决N色冰模型
Solving the n-color ice model
论文作者
论文摘要
考虑到两组$ n $颜色晶格型号的两组非零玻尔兹曼的重量，我们在这些玻尔兹曼的权重上提供明确的代数条件，以保证朝阳方程的解决方案（即，第三组重量）。此外，在这种情况下，我们提供了所有解决方案的明确的一维参数化。这些$ n $ - 色晶格型号之所以如此命名，是因为它们的可接受的顶点的边缘与$ n $颜色之一标记有额外限制。两色案例专门针对六个vertex模型，在这种情况下，我们的结果恢复了巴克斯特熟悉的二次条件以供溶解度。一般的$ n $ - 彩色案例包括对杨巴克斯特方程的重要解决方案，例如量子仿射的评估模块lie代数$ u_q（\ hat {\ mathfrak {\ mathfrak {sl}} _ n）$。最后，我们证明了在自然变换下这类解决方案的不变性，包括与德林菲尔德扭曲相关的解决方案。
Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the Yang-Baxter equation. Furthermore we provide an explicit one-dimensional parametrization of all solutions in this case. These $n$-color lattice models are so named because their admissible vertices have adjacent edges labeled by one of $n$ colors with additional restrictions. The two-colored case specializes to the six-vertex model, in which case our results recover the familiar quadric condition of Baxter for solvability. The general $n$-color case includes important solutions to the Yang-Baxter equation like the evaluation modules for the quantum affine Lie algebra $U_q(\hat{\mathfrak{sl}}_n)$. Finally, we demonstrate the invariance of this class of solutions under natural transformations, including those associated with Drinfeld twisting.
