The Grassmannian-like coset model and the higher spin currents

In the Grassmannian-like coset model, $\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$, Creutzig and Hikida have found charged spin-$2,3$ currents neutral previously. this paper, as an extension of Gaberdiel-Gopakumar conjecture ten years ago, we calculate operator product expansion (OPE) between spin-$2$ current itself, OPE spin-$3$ itself for generic $N, M$ $k$. From second OPE, obtain new quasi primary spin-$4$ while from last one, is implicitly. The infinity limit $k$ in structure constants OPEs described context asymptotic symmetry $M matrix generalization $AdS_3$ higher spin theory. Moreover, determined fixed $(N,M)=(5,4)$ with arbitrary up to third order pole. We also spin-$1,2,3$ current. realize that there exists presence above pole $(N,M)=(5,4)$. comment on complex free fermion realization.