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On the decomposition of the Foulkes module

Research paper by Eugenio Giannelli

Indexed on: 07 Mar '13Published on: 07 Mar '13Published in: Archiv der Mathematik



Abstract

The Foulkes module \({H^{(a^b)}}\) is the permutation module for the symmetric group Sab given by the action of Sab 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 \({\mathbb{C} S_{ab}}\) -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, 1r) with r ≥ 1 appears in \({H^{(a^b)}}\) .