English

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).

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Cite

@article{arxiv.1207.6300,
  title  = {On the decomposition of the Foulkes module},
  author = {Eugenio Giannelli},
  journal= {arXiv preprint arXiv:1207.6300},
  year   = {2012}
}