On the structure of Specht modules in the principal block of FΣ3p

JOURNAL OF ALGEBRA

卷:448

Article

Rosas, Michael¹ 

[1] SUNY Buffalo, Univ Buffalo, Dept Math, 244 Math Bldg, Buffalo, NY 14260 USA

关键词: Symmetric group;    Specht module;   

DOI  :  10.1016/j.jalgebra.2015.10.003

来源: Elsevier

【 摘 要 】

Let F be a field of characteristic p at least 5. We study the Loewy structures of Specht modules in the principal block of F Sigma(3p). We show that a Specht module in the block has Loewy length at most 4 and composition length at most 14. Furthermore, we classify which Specht modules have Loewy length 1, 2, 3, or 4, produce a Specht module having 14 composition factors, describe the second radical layer and the socle of the reducible Specht modules, and prove that if a Specht module corresponds to a partition that is p-regular and p-restricted then the head of the Specht module does not extend the socle. (C) 2015 Published by Elsevier Inc.

【 授权许可】

Free