论文标题
四维晶格，相关矩阵差方程及其解决方案的平坦连接
Flat connection on four-dimensional lattice, related matrix difference equations and their solutions
论文作者
论文摘要
在论文中[ 51（2018）445202]通过降低的量子Knizhnik-Zamolodchikov方程，计算了SL（3）-SL（3）-Invariant基本交换模型的密度降低。在本文中，我们介绍了一些特殊差异问题的解决方案，起源于操作员长度4的密度矩阵的研究。这个差异问题与四维零外面的条件有关，并且明确的几何含义是我们具有琐碎的光纤束cp^3 x c^4具有载体的载体功能，该载体具有C^4和Space coptive cp^33 33的载体。局部连接系数满足上述零曲率或平坦条件的满足。我们在此讨论的解决方案是根据伽马功能（其对数衍生物，超几何函数和通过差异类型功能关系定义的其他相关功能）提供的。
In the paper [H.Boos, A.Hutsalyuk and Kh.Nirov, J.Phys.A:Math.Theor. 51 (2018) 445202] the reduced density matrix of the sl(3)-invariant fundamental exchange model was calculated for the operator length up to three by means of the reduced quantum Knizhnik-Zamolodchikov equation. In this paper we present the solution of some special difference problem originated from the study of the reduced density matrix for the operator length 4. This difference problem is related to a four-dimensional zero-curvature condition and has a clear geometrical meaning were we have a trivial fiber bundle CP^3 x C^4 with a vector function which takes value in C^4 and the base being the projective space CP^3. The local connection coefficients satisfy the above mentioned zero-curvature or flatness condition. The solution we discuss here is given in terms of the Gamma-function, its logarithmic derivative, hypergeometric functionand some other related functions defined via the functional relations of difference type.
