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Specht modules with abelian vertices (1102.2484v2)
Published 12 Feb 2011 in math.RT
Abstract: In this article, we consider indecomposable Specht modules with abelian vertices. We show that the corresponding partitions are necessarily $p2$-cores where $p$ is the characteristic of the underlying field. Furthermore, in the case of $p\geq 3$, or $p=2$ and $\mu$ is 2-regular, we show that the complexity of the Specht module $S\mu$ is precisely the $p$-weight of the partition $\mu$. In the latter case, we classify Specht modules with abelian vertices. For some applications of the above results, we extend a result of M. Wildon and compute the vertices of the Specht module $S{(pp)}$ for $p\geq 3$.