Automorphism group of parafermion vertex operator algebras

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.