The geometric Burge correspondence and the partition function of polymer replicas
The geometric Burge correspondence and the partition function of polymer replicas
Abstract We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge correspondence, specializing …