量子Knizhnik-Zamolodchikov方程、广义Razumov-Stroganov求和规则和推广的Joseph多项式
Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
摘要：
我们证明了更高的秩类似物的Razumov-Stroganov和规则的基态的O（1）循环模型在半无限圆柱：我们表明，加权和的分量的基态的A_{k-1} IRF模型产生整数，概括的交替符号矩阵的数量。这是通过构造一级U_q（\hat{sl(k)}）量子Knizhnik-Zamolodchikov方程的极小多项式解来实现的，它也可以解释为分数量子霍尔效应波函数在填充分数nu=1/k时的量子不可压缩q变形.除了广义Razumov-Stroganov点q=-e^{i pi/k+1}之外，在有理极限q ->-1中达到了另一个组合上有趣的点，其中我们用与具有零k次幂的上三角矩阵的几何相关联的扩展约瑟夫多项式来识别解。
英文摘要：
We prove higher rank analogues of the Razumov--Stroganov sum rule for the groundstate of the O(1) loop model on a semi-infinite cylinder: we show that a weighted sum of components of the groundstate of the A_{k-1} IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 U_q(\hat{sl(k)}) quantum Knizhnik--Zamolodchikov equations, which may also be interpreted as quantum incompressible q-deformations of fractional quantum Hall effect wave functions at filling fraction nu=1/k. In addition to the generalized Razumov--Stroganov point q=-e^{i pi/k+1}, another combinatorially interesting point is reached in the rational limit q -> -1, where we identify the solution with extended Joseph polynomials associated to the geometry of upper triangular matrices with vanishing k-th power.
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