ϕ-Coordinated modules for quantum vertex algebras and associative algebras

We study N-graded ϕ-coordinated modules for a general quantum vertex algebra V of a certain type in terms of an associative algebra A˜(V) introduced by Y.-Z. Huang. Among the main results, we associate a sequence of associative algebras A˜n(V) for n∈N with A˜0(V)=A˜(V) and we establish a bijection between the set of equivalence classes of irreducible N-graded ϕ-coordinated V-modules and the set of isomorphism classes of irreducible A˜(V)-modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector.