发表机构
National Institute of Technology, Akashi College（明石国立技术大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了集值斜杨表、标记Gelfand-Tsetlin模式与五顶点模型装饰态之间的双射，保持权重并交织晶体算子，证明了纤维的布尔格结构及符号反转对合的性质。
AI 中文摘要
我们构造了斜形状的半标准集值杨表、带标记的Gelfand-Tsetlin模式以及由斜形状确定边界数据的五顶点模型的装饰态之间的双射。这些双射保持单项式权重，将杨表的超出量（excess）与标记数和非平凡凸起数对应起来，并将通常的A型晶体算子与装饰态的局部变换相互交织。我们证明了由固定最大杨表确定的每个纤维是一个分次布尔格，其秩函数为超出量。其加权生成函数具有乘积公式。符号反转对合在每个它不固定的杨表上改变一个布尔坐标，我们确定了它与所有升算子以及与除涉及被改变项的两个颜色外的降算子的交换性。我们构造了与最小项相关的对偶对合，并证明了由固定最小杨表确定的纤维以及具有规定最小和最大杨表的纤维的相应布尔结构。
英文摘要
We prove commutation relations between the ordinary type A crystal operators and a sign-reversing involution on semistandard set-valued tableaux of skew shape. We describe the involution by Boolean fibers with fixed maximum entries. It commutes with every raising operator except the one indexed by the entry changed by the involution. We characterize commutation at this exceptional raising operator and for lowering operators away from the two colors involving that entry using the box where the involution acts and reduced signatures. We construct a bijection from these tableaux to decorated five-vertex states that preserves weight and excess, subject to a restriction on nontrivial bumps determined by the inner partition. Rotation with alphabet reversal yields the dual statements.
Comments34 pages, 6 figures
