论文标题
Gelfand $ s_n $ -graphs的插入算法
Insertion algorithms for Gelfand $S_n$-graphs
论文作者
论文摘要
当且仅当输入排列是一项互动时，Robinson-Schensted对应分配的两个表达是相等的，因此RS算法限制了对称组和标准tableaux中的互动之间的两次试验。 Beissinger找到了制定此限制地图的简洁方法，该方法涉及在Schensted插入过程之后在一排末端添加一个额外的单元格。我们表明，通过稍微更改此算法以在列的末尾添加细胞而不是行，人们可以从与标准的tableaux相处获得不同的生命。这两个地图与表示理论都有有趣的联系。具体而言，我们的插入算法将与通用对称组的唯一等效模型相关的$ w $绘图对分子进行了分类（并构想的细胞）。
The two tableaux assigned by the Robinson--Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection between involutions in the symmetric group and standard tableaux. Beissinger found a concise way of formulating this restricted map, which involves adding an extra cell at the end of a row after a Schensted insertion process. We show that by changing this algorithm slightly to add cells at the end of columns rather than rows, one obtains a different bijection from involutions to standard tableaux. Both maps have an interesting connection to representation theory. Specifically, our insertion algorithms classify the molecules (and conjecturally the cells) in the pair of $W$-graphs associated to the unique equivalence class of perfect models for a generic symmetric group.
