Set families and Foulkes modules

Details Set families and Foulkes modules Set families and Foulkes modules

2010-07-17

arxiv.org/abs/1007.2946v1

Mathematics

Representation Theory

22 pages, 3 figures

Scientific paper

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label irreducible characters appearing as summands of the characters of Foulkes modules. The homomorphisms are defined using certain families of subsets of the natural numbers. These families are of independent interest; we prove a number of combinatorial results concerning them.

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