Representations of vertex operator algebras and bimodules

For a vertex operator algebra V, a V-module M and a nonnegative integer n, an An(V)-bimodule An(M) is constructed and studied. The connections between An(M) and intertwining operators are discussed. Moreover, the An(V)-bimodule At,s(V) is a quotient of An(V) for all s,t⩽n. In the case that V is rational, An(M) for irreducible V-module M is given explicitly.