The first part of this article is an informal introduction to the representation theory of the symmetric group, which is intended for the working mathematician who knows no representation theory. In the second part we explain, more generally, how representation theory can be used to study symplectic quotient singularities. Namely, one can use representation theory to decide when these singular spaces admit crepant resolutions.
Keywords
Representation theory, symmetric group, quotient singularities, crepant resolutions, finite groups, algebraic geometry.