On Schur Functions, Tableaux and the Littlewood–Richardson Rule

Sammanfattning

The object of this report is the study of symmetric functions, with particular emphasis on Schurfunctions. In our study of these functions, we encounter objects such as partitions, Ferrers diagramsand Young tableaux and explore the interplay between these. We establish through the Knuth Correspondence a relationship between matrices and tableaux, which is then used to derive Littlewood’s Theorem. In the final chapter, we use this theorem to obtain the Littlewood–Richardson coefficients. Together with the Littlewood–Richardson Rule, these coefficients permit the calculation ofproducts of Schur functions.