On the decomposition of the Foulkes module |
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Authors: | Eugenio Giannelli |
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Institution: | 1. Royal Holloway, University of London, London, UK
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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 ${\mathbb{C} S_{ab}}$ -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, 1 r ) with r ≥ 1 appears in ${H^{(a^b)}}$ . |
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