Colored five-vertex models and Lascoux polynomials and atoms
Abstract
We construct an integrable colored five-vertex model whose partition function is a Lascoux atom based on the five-vertex model of Motegi and Sakai [arXiv:1305.3030] and the colored five-vertex model of Brubaker, the first author, Bump, and Gustafsson [arXiv:1902.01795]. We then modify this model in two different ways to construct a Lascoux polynomial, yielding the first known combinatorial interpretation of a Lascoux polynomial and atom. Using this, we prove a conjectured combinatorial interpretation in terms of set-valued tableaux of a Lascoux polynomial and atom due to Pechenik and the second author [arXiv:1904.09674]. We also prove the combinatorial interpretation of the Lascoux atom using set-valued skyline tableaux of Monical [arXiv:1611.08777].
Cite
@article{arxiv.1908.07364,
title = {Colored five-vertex models and Lascoux polynomials and atoms},
author = {Valentin Buciumas and Travis Scrimshaw and Katherine Weber},
journal= {arXiv preprint arXiv:1908.07364},
year = {2020}
}
Comments
23 pages, 7 figures; added examples and other changes from referee report