Induced modules for orbifold vertex operator algebras

Abstract

Let V be a simple vertex operator algebra and G< Aut V a finite abelian subgroup such that VG is rational. We study the representations of V based on certain assumptions on VG-modules. We prove a decomposition theorem for irreducible V-modules. We also define an induced module from VG 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.