On the decomposition of the Foulkes module

摘要

The Foulkes module H~((ab)) 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 ?S_(ab)-module to have zero multiplicity in H~((ab)). 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~((ab)).