Specht modules with abelian vertices

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≥3, or p=2 and μ is 2-regular, we show that the complexity of the Specht module Sμ 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S^{(p^{p})}$\end{document} for p≥3.