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We define restricted Schur polynomials built using both fermionic and bosonicfields which transform in the adjoint of the gauge group U(N). We show thatthese operators diagonalize the free field two point function to all orders in1/N. As an application of our new operators, we study the action of the oneloop dilatation operator in the su(2|3) sector in a large N but non-planarlimit. The restricted Schur polynomials we study are dual to giant gravitons.We find that the one loop dilatation operator can be diagonalized using adouble coset ansatz. The resulting spectrum of anomalous dimensions matches thespectrum of a set of decoupled oscillators. Finally, in an Appendix we studythe action of the one loop dilatation operator in an sl(2) sector. This actionis again diagonalized by a double coset ansatz.

Restricted Schur Polynomials for Fermions and integrability in the su(2|3) sector