On the decomposition of the Foulkes module
Representation Theory
2012-07-27 v1 Group Theory
Abstract
The Foulkes module H^(a^b) is the permutation module for the symmetric group S_ab given by the action of S_ab on the collection of set partitions of a set of size ab into b sets each of size a. The main result of this paper is a sufficient condition for a simple CS_{ab}-module to have zero multiplicity in H^(a^b). A special case of this result implies that no Specht module labelled by a hook partition (ab - r, 1^r) appears in H(a^b).
Keywords
Cite
@article{arxiv.1207.6300,
title = {On the decomposition of the Foulkes module},
author = {Eugenio Giannelli},
journal= {arXiv preprint arXiv:1207.6300},
year = {2012}
}