A charged and neutral spin-4 currents in the Grassmannian-like coset model

By calculating the second-order pole in the operator product expansion (OPE) of the charged spin-3 current with the neutral spin-3 current in the Grassmannian-like coset model, we determine the primary charged spin-4 current. Similarly, by computing the second-order pole in the OPE of the neutral spin-3 current with itself, we obtain the primary neutral spin-4 current. We determine the OPE of the charged spin-2 current with the charged spin-3 current for generic parameters and the large k (one of the parameters) limit is also obtained for this OPE. In particular, the above primary charged spin-4 current appears in the first-order pole of this OPE for generic parameters. We also check that the above primary charged and neutral spin-4 currents occur at the second-order pole in the OPE of the charged spin-3 current with itself for fixed parameters.