Specht modules with abelian vertices

Kay Jin Lim

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 \ge 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 consequences of the above results, we extend a result
by M. Wildon and compute the vertices of the Specht module 
S^{(p^p)} for p \ge 3.