Representation Theory of the Symmetric Group

Philip Foth

The symmetric group appears in many important branches of modern
mathematics and its representation theory has deep implications in
algebra, analysis, and geometry. We will review basic facts about the
representation theory of this group over the field of complex numbers.
We will describe the Young tableaux and the Robinson-Schensted
algorithm. We will also show how the symmetric group is related to the
unitary group and the reciprocity between their representation.
Finally, we outline applications to geometry and possible directions of
further studies.