The action of the symmetric group Smn on set partitions of a set of size mn into n sets of size m gives rise to a permutation module called the Foulkes module. Structurally, very little is known about Foulkes modules, even in characteristic zero. In this talk, we will see that semistandard homomorphisms may be used as a tool for studying the module structure and, in particular, for establishing relationships between irreducible constituents of Foulkes modules.
Studying Foulkes modules using semistandard homomorphisms
Melanie de Boeck (Kent)
Mon, 13/10/2014 - 17:30