Abstract
In a recent letter, new representations were proposed for the pair of sequences (γ,δ), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (γ,δ) labelled by the Lie algebra AN − 1, two nonnegative integers ℓ and k and a partition λ, 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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Schilling, A., Ole Warnaar, S. A Higher Level Bailey Lemma: Proof and Application. The Ramanujan Journal 2, 327–349 (1998). https://doi.org/10.1023/A:1009746932284
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DOI: https://doi.org/10.1023/A:1009746932284