2017/07/31 by Ian Le, Le, Ian
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1708.00780
openalex publication_date 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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=SLn. 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.