Dimers, webs, and local systems

Abstract

For a planar bipartite graph G \mathcal {G} equipped with an S L n \mathrm {SL}_n -local system, we show that the determinant of the associated Kasteleyn matrix counts “ n n -multiwebs” (generalizations of n n -webs) in G \mathcal {G} , weighted by their web-traces. We use this fact to study random n n -multiwebs in graphs on some simple surfaces.