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We generalize the Goddard-Kent-Olive (GKO) coset construction to thedimension 5/2 operator for $ \hat{so} (5) $ and compute the fourth order  Casimir invariant in the coset model $\hat{SO} (5)_{1} \times \hat{SO}(5)_{m} / \hat{SO} (5)_{1+m} $ with the generic unitary minimal $ c < 5/2 $series that can be viewed as perturbations of the $ m \rightarrow \infty $limit, which has been investigated previously in the realization of $ c= 5/2 $free fermion model.Comment: 11 page

Explicit construction of the spin-4 Casimir operator in the coset model SO(5)1*SO(5)m/SO(5)1+m

Explicit construction of the spin-4 Casimir operator in the coset model SO(5)₁*SO(5)_m/SO(5)_1+m