A colored five-vertex model has Lascoux atom and polynomial partition functions, proving the Pechenik-Scrimshaw and Monical set-valued tableau conjectures.
Colored five-vertex models and Demazure atoms
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abstract
Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a biproduct, we construct Demazure atoms on Kashiwara's $\mathcal{B}_\infty$ crystal and give new algorithms for computing Lascoux-Sch\"utzenberger keys.
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math.CO 1years
2019 1verdicts
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Colored five-vertex models and Lascoux polynomials and atoms
A colored five-vertex model has Lascoux atom and polynomial partition functions, proving the Pechenik-Scrimshaw and Monical set-valued tableau conjectures.