An insertion algorithm on multiset partitions with applications to diagram algebras
An insertion algorithm on multiset partitions with applications to diagram algebras
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DOI：
10.1016/j.jalgebra.2020.04.010
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发表时间：
2019-05
影响因子：
0.9
通讯作者：
L. Colmenarejo;R. Orellana;Franco V. Saliola;A. Schilling;M. Zabrocki
中科院分区：
文献类型：
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作者：
L. Colmenarejo;R. Orellana;Franco V. Saliola;A. Schilling;M. Zabrocki
摘要本文将Robinson-Schensted-Knuth算法推广到多集的两行数组插入问题。这种推广导致新的枚举结果，有表示理论的解释分解的中心化代数和空间，他们的作用。此外，限制的多集导致进一步的身份和表示理论的类似物。例如，我们得到了长度为k的词与条目在[n]中的词之间的双射，以及相同形状的表对，其中一个是大小为n的标准Young表，另一个是内容为[k]的标准多集表。我们还获得了一个算法从分区图对一个标准的表和一个标准的多集表相同的形状，它具有显着的属性，它是良好的行为方面限制表示的子代数。该插入算法与Halverson和Jacobson [15]的最新表示理论结果相匹配。
Abstract We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer algebras and the spaces they act on. In addition, restrictions on the multisets lead to further identities and representation theory analogues. For instance, we obtain a bijection between words of length k with entries in [n] and pairs of tableaux of the same shape with one being a standard Young tableau of size n and the other being a standard multiset tableau of content [k]. We also obtain an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic results of Halverson and Jacobson [15].