Bimodules associated to vertex operator algebras

Let V be a vertex operator algebra and m, n >= 0. We construct an A(n) (V)-A(m) (V)-bimodule A(n,m) (V) which determines the action of V from the level m subspace to level n subspace of an admissible V-module. We show how to use A(n,m) (V) to construct naturally admissible V-modules from A(m) (V)-modules. We also determine the structure of A(n,m)(V) when V is rational.