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 byproduct, we will construct Demazure atoms on Kashiwara's B∞ crystal and give new algorithms for computing Lascoux-Schützenberger keys.
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Acknowledgments: This work was supported by NSF grants DMS-1801527 (Brubaker) and DMS-1601026 (Bump). Buciumas was supported by ARC grant DP180103150 . During his time at Stanford University (when this paper was written), Gustafsson was supported by the Knut and Alice Wallenberg Foundation . We thank Amol Aggarwal, Alexei Borodin, Vic Reiner, Anne Schilling, Michael Wheeler and Matthew Willis for helpful conversations and communications. We thank the referees for useful comments which improved the exposition of the paper.
- Demazure atom
- Lattice model
- LS keys
- The Yang-Baxter equation