Automorphism group of parafermion vertex operator algebras

Abstract

The automorphism group of parafermion vertex operator algebra associated with the irreducible highest weight module for the affine Kac–Moody algebra A1(1) was easily determined since the Virasoro primary vector of weight 3 in this parafermion vertex operator algebra is unique up to a scalar. However, it is highly nontrivial to determine the automorphism group of parafermion vertex operator algebra associated with the irreducible highest weight module for the affine Kac–Moody algebra An(1) with the rank n≥2. As the first step, in this paper, we determine the full automorphism group of parafermion vertex operator algebra associated with the irreducible highest weight module for the affine Kac–Moody algebra A2(1), which shows the idea for a complete determination for the full automorphism group of the parafermion vertex operator algebra associated with the irreducible highest weight module for any affine Kac–Moody algebra.