Straightening and Foulkes' conjecture

The textbook constructions of the irreducible representations of the symmetric group and the polynomial irreducible representations of the general linear group rely on a process called straightening. This straightening process expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. I will present a purely combinatorial construction of these representations and illustrate how straightening is used. I will then show how straightening can be used to compute multiplicities of irreducible representations in certain plethysms and discuss how this can be used to study Foulkes' conjecture.