A Higher-Level Bailey Lemma: Proof and Application

Details A Higher-Level Bailey Lemma: Proof and Application A Higher-Level Bailey Lemma: Proof and Application

1996-07-12

arxiv.org/abs/q-alg/9607014v2

Mathematics

Quantum Algebra

Latex2e, 21 pages, 1 Postscript figure. Several typos have been corrected including a serious one, a figure has been added and

Scientific paper

In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), 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 non-negative integers $\ell$ and $k$ and a partition $\lambda$, whose parts do not exceed $N-1$. Our results give rise to what we call a ``higher-level'' Bailey lemma. As an application it is shown how this lemma can be applied to yield general $q$-series identities, which generalize some well-known results of Andrews and Bressoud.

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