Specht modules with abelian vertices

Details Specht modules with abelian vertices Specht modules with abelian vertices

2011-02-12

arxiv.org/abs/1102.2484v2

Mathematics

Representation Theory

Scientific paper

10.1007/s10801-011-0298-0

In this article, we consider indecomposable Specht modules with abelian vertices. We show that the corresponding partitions are necessarily $p^2$-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 $S^{(p^p)}$ for $p\geq 3$.

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