The VOAs generated by two Ising vectors e and f with <e,f>=1/2^8 or 3/2^9

Abstract

In this paper we study the VOAs generated by two Ising vectors whose inner product is 1/2^8 or 3/2^9 and determine they both have unique VOA structures.

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• Sigma involutions associated with parafermion vertex operator algebra $K({\mathfrak{sl}}_2,k)$