  In a recent work, restricted Schur polynomials have been argued to form a
complete orthogonal set of gauge invariant operators for the 1/4-BPS sector of
free N = 4 super Yang-Mills theory with an SO(N) gauge group. In this work, we
extend these results to the theory with an Sp(N) gauge group. Using these
operators, we develop techniques to compute correlation functions of any
multi-trace operators with two scalar fields exactly in the free theory limit
for both SO(N) and Sp(N).
