论文标题
仙人掌群对偏移的图形晶体的作用
An action of the cactus group on shifted tableau crystals
论文作者
论文摘要
最近，吉莱斯皮（Gillespie），莱文森（Levinson）和普尔布胡（Purbhoo）引入了一种晶体样结构，用于移动的tableaux，称为移动的图型晶体。我们介绍了晶体反射算子的转移类似物，这与施换后的Schützenberger相互作用的限制到两个相邻字母的任何启动间隔相吻合。与$ a $ a $ a $ young Tableau Crystals不同，这些运营商没有意识到对称群体在转移的Tableau Crystal上的行动，因为编织关系不存在。我们表现出仙人掌群的自然内部作用，这是通过在基础晶体字母的启动间隔内限制了schützenberger的限制。
Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce a shifted analogue of the crystal reflection operators, which coincides with the restriction of the shifted Schützenberger involution to any primed interval of two adjacent letters. Unlike type $A$ Young tableau crystals, these operators do not realize an action of the symmetric group on the shifted tableau crystal because braid relations do not hold. We exhibit a natural internal action of the cactus group, realized by restrictions of the shifted Schützenberger involution on primed intervals of the underlying crystal alphabet.
