Integrable systems and crystals for edge labeled tableaux

Abstract

We introduce the edge Schur functions $E^{\lambda }$ that are defined as a generating series over edge labeled tableaux. We formulate $E^{\lambda }$ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of $E^{\lambda }$ and show it intertwines with an uncrowding algorithm.

arXiv comment29 pages, 2 figures

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