论文标题
Socle Tableau是Littlewood-Richardson Tableau的双重版本
The socle tableau as a dual version of the Littlewood-Richardson tableau
论文作者
论文摘要
像LR-Tableau一样，Socle Tableau被作为带有某些条目的偏斜图。与LR-Tableau不同，Socle Tableau的条目在每一行的弱增加，严格增加了每一列，并满足修改后的晶格置换属性。在有限的Abelian $ p $ - 组中亚组的嵌入的研究中，Socle tableaux作为同构不变性出现，它们是由亚组的Socle系列给出的。我们表明，每个Socle Tableau都可以通过某些嵌入来实现。此外，嵌入的Socle Tableau和双嵌入的LR-Tableau相互决定。
Like the LR-tableau, a socle tableau is given as a skew diagram with certain entries. Unlike in the LR-tableau, the entries in the socle tableau are weakly increasing in each row, strictly increasing in each column and satisfy a modified lattice permutation property. In the study of embeddings of a subgroup in a finite abelian $p$-group, socle tableaux occur as isomorphism invariants, they are given by the socle series of the subgroup. We show that each socle tableau can be realized by some embedding. Moreover, the socle tableau of an embedding and the LR-tableau of the dual embedding determine each other.
