Grassmannian中的可积离散网
Integrable discrete nets in Grassmannians
摘要：
我们考虑离散网在格拉斯曼$\mathbb{G}^d_r$推广Q-网（地图$\mathbb{Z}^N\to\mathbb{P}^d$与平面基本四边形）和达布网（$\mathbb{P}^d$值的地图上定义的边缘$\mathbb{Z}^N$，使四重点对应的基本正方形都是共线的）。我们给出了这些新的网络的可积性（多维一致性）的几何证明，并表明它们是由非交换离散达布系统解析描述的。
英文摘要：
We consider discrete nets in Grassmannians $\mathbb{G}^d_r$ which generalize Q-nets (maps $\mathbb{Z}^N\to\mathbb{P}^d$ with planar elementary quadrilaterals) and Darboux nets ($\mathbb{P}^d$-valued maps defined on the edges of $\mathbb{Z}^N$ such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability (multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete Darboux system.
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