论文标题
超级鲁滨逊 - 史密斯·斯诺特（Super Robinson-Schensted-Knuth）与对称和超级小伍德 - 里奇森（Super Littlewood-Richardson）统治
A super Robinson-Schensted-Knuth correspondence with symmetry and the super Littlewood-Richardson rule
论文作者
论文摘要
Robinson-Schensted-Knuth（RSK）对应关系是非阴性整数的两行阵列与相同形状的Semistandard Tableaux对的两行对应关系。这种对应关系满足对称属性，即交换两行阵列的行等于交换相应的Semistandard Tableaux对的位置。在本文中，我们使用Schensted的插入算法的超级版本介绍了签名的字母上的RSK信函的超级类似物。我们通过矩阵构造对Super-RSK对应进行了几何解释，以完全普遍性显示了对称属性。我们推断出有限签名字母的Super Schur功能的Super Littlewood-Richardson规则的组合版本。最后，我们介绍了Super Littlewood-Richardson Skew Tableaux的概念，并对Super Littlewood-Richardson Rule进行了另一种组合解释。
Robinson-Schensted-Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of non-negative integers and pairs of same-shape semistandard tableaux. This correspondence satisfies the symmetry property, that is, exchanging the rows of a two-rowed array is equivalent to exchanging the positions of the corresponding pair of semistandard tableaux. In this article, we introduce a super analogue of the RSK correspondence for super tableaux over a signed alphabet using a super version of Schensted's insertion algorithms. We give a geometrical interpretation of the super-RSK correspondence by a matrix-ball construction, showing the symmetry property in complete generality. We deduce a combinatorial version of the super Littlewood-Richardson rule on super Schur functions over a finite signed alphabet. Finally, we introduce the notion of super Littlewood-Richardson skew tableaux and we give another combinatorial interpretation of the super Littlewood-Richardson rule.
