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arXiv · 2202.06004

Integrable systems and crystals for edge labeled tableaux

Ajeeth Gunna·Travis Scrimshaw
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Abstract

We introduce the edge Schur functions $E^λ$ that are defined as a generating series over edge labeled tableaux. We formulate $E^λ$ 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 $E^λ$ and show it intertwines with an uncrowding algorithm.

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Ajeeth Gunna, Travis Scrimshaw. 2022-02-12. Integrable systems and crystals for edge labeled tableaux. https://doi.org/10.1016/j.jalgebra.2023.12.031

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