On the higher-rank dimer model

Richard Kenyon
Yale University

On a planar bipartite graph with a
GL(n) local system, we define an associated Kasteleyn operator
and show that its determinant counts traces of “n-multiwebs”,
which are combinatorial objects generalizing dimer configurations
(which correspond to the case n=1).
For SL(3) we compute connection probabilities in the scaling limit
and show their conformal invariance.
This is based joint works with Dan Douglas and Haolin Shi.

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