The operator product expansion of the lowest higher spin current at finite N

For the N = 2 Kazama-Suzuki(KS) model on CP3, the lowest higher spin current with spins (2, 5/2, 5/2, 3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N = 2 WN+1 algebra with N = 3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N, k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N = 2 KS model on CPN space. This should coincide with the asymptotic symmetry of the higher spin AdS(3) supergravity at the quantum level. The large (N, k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.