Representation theory of the symmetric group

Summary

The representation theory of the symmetric group $S_n$ studies its representations and characters. Over the complex numbers, the irreducible representations of $S_n$ correspond to the partitions of $n$, and are realised by the Specht modules. The theory is fully combinatorial: Young diagrams and Young tableaux give dimensions and characters. It connects with symmetric functions, the representations of general linear groups and many parts of combinatorics and physics.