Induced modules for orbifold vertex operator algebras

Abstract

Let $V$ be a simple vertex operator algebra and Aut $V$ a finite abelian subgroup such that $V^G$ is rational. We study the representations of $V$ based on certain assumptions on $V^G$-modules. We prove a decomposition theorem for irreducible $V$-modules. We also define an induced module from $V^G$ to $V$ and show that every irreducible $V$-module is a quotient module of some induced module. In addition, we prove that $V$ is rational in this case.