Specht modules with abelian vertices

Abstract

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≥3, or p=2 and μ is 2-regular, we show that the complexity of the Specht module S μ is precisely the p-weight of the partition μ. 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≥3. © 2011 Springer Science+Business Media, LLC.