  We compute the one loop anomalous dimensions of restricted Schur polynomials
with a classical dimension \Delta\sim O(N). The operators that we consider are
labeled by Young diagrams with two long columns or two long rows. Simple
analytic expressions for the action of the dilatation operator are found. The
projection operators needed to define the restricted Schur polynomials are
constructed by translating the problem into a spin chain language, generalizing
earlier results obtained in the SU(2) sector of the theory. The diagonalization
of the dilatation operator reduces to solving five term recursion relations.
The recursion relations can be solved exactly in terms of products of symmetric
Kravchuk polynomials with Hahn polynomials. This proves that the dilatation
operator reduces to a decoupled set of harmonic oscillators and therefore it is
integrable, extending a similar conclusion reached for the SU(2) sector of the
theory.
