Higher spin currents in the N=2 stringy coset minimal model

In the coset model based on (AN-1(1)-AN-1(1),AN-1(1)) at level (N,N;2N), it is known that the N=2 superconformal algebra can be realized by the two kinds of adjoint fermions. Each Kac-Moody current of spin 1 is given by the product of fermions with structure constant (f symbols) as usual. One can construct the spin-1 current by combining the above two fermions with the structure constant and the spin-1 current by multiplying these two fermions with a completely symmetric SU(N) invariant tensor of rank 3 (d symbols). The lowest higher spin-2 current with nonzero U(1) charge (corresponding to the zero mode eigenvalue of the spin-1 current of N=2 superconformal algebra) can be obtained from these four spin-1 currents in quadratic form. Similarly, the other type of lowest higher spin-2 current, whose U(1) charge is opposite to the above one, can be obtained also. Four higher spin-52 currents can be constructed from the operator product expansions (OPEs) between the spin-32 currents of N=2 superconformal algebra and the above two higher spin-2 currents. The two higher spin-3 currents can be determined by the OPEs between the above spin-32 currents and the higher spin-52 currents. Finally, the ten N=2 OPEs between the four N=2 higher spin multiplets (2,52,52,3), (2,52,52,3), (72,4,4,92), and (72,4,4,92) are obtained explicitly for generic N.