Signed Young modules and simple Specht modules

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• 作者：Susanne Danz^a ; ^{susanne.danz@ku.de} ; Kay Jin Lim^b ; ^{limkj@ntu.edu.sg}
• 关键词：Symmetric group ; Simple Specht module ; Signed Young module ; Green vertex ; Green correspondent ; Cohomological variety ; Complexity
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：369-416
• 全文大小：870 K
• 卷排序：307

文摘

By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are parametrized by certain pairs of partitions. The main result of this article establishes the signed Young module labels of simple Specht modules. Along the way we prove a number of results concerning indecomposable signed Young modules that are of independent interest. In particular, we determine the label of the indecomposable signed Young module obtained by tensoring a given indecomposable signed Young module with the sign representation. As consequences, we obtain the Green vertices, Green correspondents, cohomological varieties, and complexities of all simple Specht modules and a class of simple modules of symmetric groups, and extend the results of Gill on periodic Young modules to periodic indecomposable signed Young modules.