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On Zhu's algebra and C2–algebra for symplectic fermion vertex algebra SF(d)+

In this paper, we study the family of vertex operator algebras , known as symplectic fermions. This family is of a particular interest because these VOAs are irrational and -cofinite. We determine Zhu's algebra and show that the equality of dimensions of and the – algebra holds for (the case of was treated by T. Abe in [1]). We use these results to prove a conjecture by Y. Arike and K. Nagatomo ([8]) on the dimension of the space of one-point functions on .

Vertex algebra ; Zhu’s algebra ; Symplectic fermions

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