Sanjaye Ramgoolam, Queen Mary - London
Representation theory of symmetric groups and local operators in gauge theory

I explain how the representation theory of symmetric groups provides elegant solutions to problems related to local operators in \(N=4\) super-Yang Mills. Gauge-invariant local operators in this theory are constructed from matrices transforming in the adjoint of the U(N) gauge group. Permutations can be used to organise the operators. Characters and Clebsch-Gordan coefficients associated with representations as well as certain universal elements in the symmetric group algebras play a role in these applications. Schur-Weyl duality is also a recurrent theme.