Percentage-Avoiding, Northwest Shapes and Peelable Tableaux
Percentage-Avoiding, Northwest Shapes and Peelable Tableaux
复制标题
避免百分比、西北形状和可剥离的画面
DOI：
10.1006/jcta.1997.2841
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
M. Shimozono
中科院分区：
文献类型：
--
作者：
V. Reiner;M. Shimozono
我们证明了与正交形和更一般的%-避免形有关的Specht模和Schur模的三个结果。第一个结果（为西北形状的作者）是一个概括的Littlewood？Richardson规则，给出了%-避免型D的Specht模和Schur模中不可约重数的一个显式组合描述，并给出了D-可剥表.第二个结果给出了三个对合的集合上的可剥离tableaux表现出这些多重性的对称性对应于三个自然对合操作的集合上的%-避免形状。第三个结果给出了西北形状的Specht模和Schur模的分支规则。所有的证明都是组合的，除了在第一个结果中的关键步骤，这需要Magyar的结果的配置品种和标志Schur模的字符。
We prove three results for Specht and Schur modules associated tonorthwest shapesand the more general class of%-avoiding shapes. The first result (conjectured for northwest shapes in by the authors) is a generalization the Littlewood?Richardson rule, giving an explicit combinatorial description for the multiplicities of irreducibles in the Specht and Schur modules of a %-avoiding shapeD, in terms ofD-peelable tableaux. The second result gives three involutions on the set of peelable tableaux which exhibit the symmetries of these multiplicities corresponding to three natural involutive operations on the set of %-avoiding shapes. The third result gives branching rules for the Specht and Schur modules of northwest shapes. The proofs are all combinatorial, with the exception of a key step in the first result, which requires results of Magyar on configuration varieties and characters of flagged Schur modules.