Specht modules with Abelian vertices.

Lim, Kay Jin

Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 157-171.

Résumé

Summary: 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 $S ^{( p ^{ p})}$ S^(p^p) for $p\geq 3$.

Détail

Keywords: keywords Specht module, vertex, complexity