高阶层合板的相交配对
Intersection Pairings for Higher Laminations
摘要：
人们可以实现更高的叠层作为仿射建筑中的点的正配置。Fock和Goncharov的对偶对给出了两个Langlands对偶群$G$和$G^{\vee}$的高阶叠层对。这些配对是拓扑表面上测量的叠层之间的相交配对的推广。在$G=SL_n$的情况下，我们给出了这些交对的几何解释。特别是，我们表明，它们可以计算为最小加权网络的建设的长度。因此，我们将交集对与仿射建筑的度量结构联系起来。这证明了几个从[LO]的algorithms的关键工具是线性化版本的著名经典结果从组合，如霍尔的婚姻引理，柯尼希定理，和库恩-芒克雷斯算法。
英文摘要：
One can realize higher laminations as positive configurations of points in the affine building. The duality pairings of Fock and Goncharov give pairings between higher laminations for two Langlands dual groups $G$ and $G^{\vee}$. These pairings are a generalization of the intersection pairing between measured laminations on a topological surface. We give a geometric interpretation of these intersection pairings in the case that $G=SL_n$. In particular, we show that they can be computed as the length of minimal weighted networks in the building. Thus we relate the intersection pairings to the metric structure of the affine building. This proves several of the conjectures from [LO] The key tools are linearized versions of well-known classical results from combinatorics, like Hall's marriage lemma, Konig's theorem, and the Kuhn-Munkres algorithm.
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