  We analyse the one-loop dilatation operator with the help of the Brauer
algebra. We find some BPS operators in N=4 SYM, which are labelled by
irreducible representations of the Brauer algebra. Some of them are quarter BPS
operators. The result includes full non-planar corrections. Our construction
and proof are based on simple algebraic arguments and are carried out for any
number of fields.

High Energy Physics - Theory