论文标题
仙人掌晶体晶体的作用
An action of the cactus group of 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。我们在这种结构上介绍了晶体反射操作员的转移版本，该版本与移动的Schützenberger互动的限制相吻合到两个相邻字母的任何启动间隔。与$ a $ a $ a $ young Tableau Crystals不同，这些操作员并没有意识到对称群体在转移的Tableau Crystal上的行动，因为辫子关系不需要保持。遵循与Halacheva相似的方法，我们表现出仙人掌基团在该晶体上的天然内部作用，这是由于移动的Schützenberger涉及到基础晶体字母的所有启动间隔的限制所实现的，尤其包含移动晶体反射操作员类似物的上述动作。
Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce, on this structure, a shifted version of the crystal reflection operators, which coincide with the restrictions 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 since the braid relations do not need to hold. Following a similar approach as Halacheva, we exhibit a natural internal action of the cactus group on this crystal, realized by the restrictions of the shifted Schützenberger involution to all primed intervals of the underlying crystal alphabet, containing, in particular, the aforesaid action of the shifted crystal reflection operator analogues.
