Quarter BPS classified by Brauer algebra

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.