Razumov-Stroganov对应的单参数加细
A one-parameter refinement of the Razumov-Stroganov correspondence
摘要：
我们介绍并证明了Razumov-Stroganov对应的一个参数的改进。这是实现了全面包装的循环配置（FPL）的域推广的平方域，并赋予回转操作。我们考虑域的一个给定侧，并且FPL使得该侧上唯一的直线瓦片是黑色的。我们表明，枚举矢量与这样的FPL，加权根据直线的位置和细化根据黑色边界点的链接模式，是散射矩阵的基态，一个可积的单参数变形的O（1）稠密圈模型哈密顿量。我们展示了原始的Razumov-Stroganov对应以及Di Francesco在2004年提出的一个猜想是如何从我们的结果中得出的。
英文摘要：
We introduce and prove a one-parameter refinement of the Razumov-Stroganov correspondence. This is achieved for fully-packed loop configurations (FPL) on domains which generalize the square domain, and which are endowed with the gyration operation. We consider one given side of the domain, and FPLs such that the only straight-line tile on this side is black. We show that the enumeration vector associated to such FPLs, weighted according to the position of the straight line and refined according to the link pattern for the black boundary points, is the ground state of the scattering matrix, an integrable one-parameter deformation of the O(1) Dense Loop Model Hamiltonian. We show how the original Razumov-Stroganov correspondence, and a conjecture formulated by Di Francesco in 2004, follow from our results.
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