Colored five-vertex models and Demazure atoms
Colored five-vertex models and Demazure atoms
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DOI：
10.1016/j.jcta.2020.105354
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发表时间：
2019-02
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A型Demazure原子是Schur函数的片段，或者是权重和为这些函数的表集。受Borodin和惠勒的着色顶点模型的启发，我们将构造配分函数为Demazure原子的可解晶格模型;这一证明使用了着色五顶点模型的杨-巴克斯特方程。作为副产品，我们将在Kashiwara的B∞晶体上构造Demazure原子，并给出计算Lascoux-Schützenberger密钥的新算法。
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.