Abstract
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.
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.