Colored five-vertex models and Demazure atoms

Ben Brubaker; Valentin Buciumas; Daniel Bump; Henrik P.A. Gustafsson

doi:10.1016/j.jcta.2020.105354

Colored five-vertex models and Demazure atoms

Ben Brubaker, Valentin Buciumas, Daniel Bump, Henrik P.A. Gustafsson

School of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 byproduct, we will construct Demazure atoms on Kashiwara's B_∞ crystal and give new algorithms for computing Lascoux-Schützenberger keys.

Original language	English (US)
Article number	105354
Journal	Journal of Combinatorial Theory. Series A
Volume	178
DOIs	https://doi.org/10.1016/j.jcta.2020.105354
State	Published - Feb 2021

Bibliographical note

Funding Information:
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.

Funding Information:
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.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Demazure atom
Integrability
LS keys
Lattice model
The Yang-Baxter equation

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10.1016/j.jcta.2020.105354

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title = "Colored five-vertex models and Demazure atoms",

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 byproduct, we will construct Demazure atoms on Kashiwara's B∞ crystal and give new algorithms for computing Lascoux-Sch{\"u}tzenberger keys.",

keywords = "Demazure atom, Integrability, LS keys, Lattice model, The Yang-Baxter equation",

author = "Ben Brubaker and Valentin Buciumas and Daniel Bump and Gustafsson, {Henrik P.A.}",

note = "Funding Information: 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. Funding Information: 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. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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doi = "10.1016/j.jcta.2020.105354",

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AU - Buciumas, Valentin

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N2 - 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.

AB - 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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Colored five-vertex models and Demazure atoms

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