A higher level Bailey lemma: Proof and application

In a recent letter, new representations were proposed for the pair of seque nces (gamma,delta), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (gamma,delta) labelled by the Lie algebra A(N-1), two nonnegative integers l and k and a partition l ambda, whose parts do not exceed N - 1. Our results give rise to what we ca ll a "higher level" Bailey lemma. As an application it is shown how this le mma can be applied to yield general q-series identities, which generalize s ome well-known results of Andrews and Bressoud.