Séminaire Lotharingien de Combinatoire, 86B.61 (2022), 12 pp.

Ajeeth Gunna and Travis Scrimshaw

Crystals and Integrable Systems for Edge Labeled Tableaux

Abstract. We define an integrable five vertex model whose partition function is the generating function E^λ of edge labeled tableau of shape λ. Using this, we prove a Cauchy-type identity. We give a crystal structure on edge labeled tableau to give a positive Schur expansion of E^λ.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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