Young modules for symmetric groups
Young modules for symmetric groups
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对称群的年轻模块
DOI：
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发表时间：
2001
影响因子：
0.7
通讯作者：
K. Erdmann
中科院分区：
文献类型：
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作者：
K. Erdmann
设K是特征为p的域，与n的划分有关的置换模，通常表示为Mλ，它不仅对对称群起着中心作用，而且通过Schur代数对一般线性群起着中心作用。这些Mλ的不可分解的直接和是由詹姆斯参数化的；它们现在被称为Young模；Klyachko和Grabmeier为Young模发展了一个‘绿色对应’。最初的参数化用的是舒尔代数；詹姆斯说，他不知道只用对称群的表示理论的证明。我们将仅使用对任意有限群有效的Brauer结构来给出这样的证明，同时我们也将证明相应的结果。
Abstract Let K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as Mλ, play a central role not only for symmetric groups but also for general linear groups, via Schur algebras. The indecomposable direct summands of these Mλ were parametrized by James; they are now known as Young modules; and Klyachko and Grabmeier developed a ‘Green correspondence’ for Young modules. The original parametrization used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.