论文标题
偏向角色和循环筛分
Skew characters and cyclic sieving
论文作者
论文摘要
在2010年，Rhoades证明了促进与矩形标准幼小tableaux相关的假程多项式的促进，从而实例了循环筛分现象。 我们将此结果扩展到所有偏斜的标准年轻tableaux，在该图案中，假程多项式评估统一根部的非负整数，尽管无法指定明确的组动作。换句话说，我们确定在哪些情况下，对称组的偏斜特征携带循环基团的排列表示。 我们使用N. Amini提出的一种方法和第一作者，该方法构成了偏斜形状边界串tableaux的数量的结合。 最后，我们将结果应用于一般线性群体伴随表示的张量幂理论。特别是，我们证明了排列之间存在两次循环介绍和促进的J.Stembridge交替的tableaux之间的两者。
In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young tableaux where the fake-degree polynomial evaluates to nonnegative integers at roots of unity, albeit without being able to specify an explicit group action. Put differently, we determine in which cases a skew character of the symmetric group carries a permutation representation of the cyclic group. We use a method proposed by N. Amini and the first author, which amounts to establishing a bound on the number of border-strip tableaux of skew shape. Finally, we apply our results to the invariant theory of tensor powers of the adjoint representation of the general linear group. In particular, we prove the existence of a bijection between permutations and J. Stembridge's alternating tableaux, which intertwines rotation and promotion.
