A Higher Level Bailey Lemma: Proof and Application |
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| Authors: | Schilling Anne Ole Warnaar S |
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| Institution: | (1) Institute for Theoretical Physics, State University of New York, Stony Brook, NY 11794-3840, USA;(2) Present address: Instituut voor Theoretische Fysica, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands. Email;(3) Mathematics Department, University of Melbourne Parkville, Victoria, 3052, Australia |
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| Abstract: | In a recent letter, new representations were proposed for the pair of sequences ( , ), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers  and k and a partition  , 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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| Keywords: | q-series Bailey's lemma Rogers-Ramanujan identities |
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