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 ${\mathcal{B}}_{\infty }$ crystal and give new algorithms for computing Lascoux-Schützenberger keys.

中文翻译：

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彩色五顶点模型和Demazure原子

类型A的Demazure原子是Schur函数的一部分，或者是权重总和等于此类函数的一组tableaux。受Borodin和Wheeler的彩色顶点模型的启发，我们将构建分配函数为Demazure原子的可解晶格模型。对此的证明是将Yang-Baxter方程用于彩色五顶点模型。作为副产品，我们将在柏原的${\mathcal{乙}}_{\infty }$ 晶体，并提供了用于计算Lascoux-Schützenberger密钥的新算法。