Research on irreducible representations of W-algebras by using lattice vertex operator algebras

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We study parafermion vertex operator algebras, which form an important family of W-algebras. Its irreducible modules are constructed by using the theory of lattice vertex operator algebras. The operator product expansions among the four generators are obtained. Moreover, the singular vectors of weight 8, 9, and 10 are determined. In the case of small level k, we calculate another singular vector of weight k+1. We use the singular vector to classify the irreducible modules and establish rationality and C2-cofiniteness.