Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-11-30 , DOI: 10.1142/s0219199720500868
Dražen Adamović; Antun Milas; Qing Wang

We study parafermion vertex algebras $N−3/2(𝔰𝔩(2))$ and $N−3/2(𝔰𝔩(3))$. Using the isomorphism between $N−3/2(𝔰𝔩(3))$ and the logarithmic vertex algebra $𝒲0(2)A2$ from [D. Adamović, A realization of certain modules for the $N=4$ superconformal algebra and the affine Lie algebra $A2(1)$, Transform. Groups21(2) (2016) 299–327], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra $𝒲(2,3)$ of central charge $c=−10$, and that $N−3/2(𝔰𝔩(3))$ is a direct sum of irreducible $N−3/2(𝔰𝔩(2))$-modules. As a byproduct, we prove certain conjectures about the vertex algebra $𝒲0(p)A2$. We also obtain a vertex-algebraic proof of the irreducibility of a family of $𝒲(2,3)c$ modules at $c=−10$.

level（2）和𝔰𝔩（3）的ferfermion顶点代数在水平-3 2上

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