On the decomposition of the Foulkes module

2012/07/26 by Giannelli, Eugenio
#20C30 (Primary) 20C15 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1207.6300

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).

Related

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