Automorphism Groups of Parafermion Vertex Operator Algebras: General Case

Abstract We complete the program for determining the full automorphism groups of all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels. We show that the full automorphism group of the parafermion vertex operator algebra is isomorphic to the automorphism group of the associated root system for the remaining cases: (i) the level is at least $3$; and (ii) the level is $2$ and the simple Lie algebra is non-simply laced.