Sigma involutions associated with parafermion vertex operator algebra

Abstract

An irreducible module for the parafermion vertex operator algebra is said to be of σ-type if an automorphism of the fusion algebra of of order k is trivial on it. For any integer k ≥ 3, we show that there exists an automorphism of order 2 of the subalgebra of the fusion algebra of spanned by the irreducible direct summands of σ-type irreducible -modules, where θ is an involution of . We discuss some examples of such an automorphism as well.