On permutation modules and decomposition numbers of the symmetric group

JOURNAL OF ALGEBRA

卷:422

Article

Giannelli, Eugenio

关键词: Representation theory;    Symmetric group;    Decomposition numbers;    Foulkes module;   

DOI  :  10.1016/j.jalgebra.2014.09.019

来源: Elsevier

【 摘 要 】

We study the indecomposable summands of the Foulkes permutation module obtained by inducing the trivial F(S-a integral S-n)-module to the full symmetric group S-an for any field F of odd prime characteristic p such that a < p <= n. In particular, we characterize the vertices of such indecomposable summands. As a corollary we disprove a modular version of Foulkes' Conjecture. In the second part of the article we use this information to give a new description of some columns of the decomposition matrices of symmetric groups in terms of the ordinary character phi(a(n)) of the Foulkes permutation module. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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