Automorphism groups of parafermion vertex operator algebras: general case

TL;DR

This paper determines the automorphism groups of all parafermion vertex operator algebras linked to simple Lie algebras, showing they correspond to the automorphism groups of their root systems in most cases.

Contribution

It completes the classification of automorphism groups for all parafermion vertex operator algebras associated with simple Lie algebras and positive integral levels.

Findings

Automorphism groups match root system automorphisms for levels ≥ 3.

Automorphism groups match root system automorphisms for level 2 if Lie algebra is non simply laced.

The classification covers all remaining cases for these algebras.

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 $3$; (ii) the level is $2$ and the simple Lie algebra is non simply laced.