dorsal/arxiv
View SchemaA Higher-Level Bailey Lemma: Proof and Application
| Authors | Anne Schilling, S. Ole Warnaar |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9607014 |
| URL | https://arxiv.org/abs/q-alg/9607014 |
Abstract
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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"abstract": "In a recent letter, new representations were proposed for the pair of\nsequences ($\\gamma,\\delta$), as defined formally by Bailey in his famous lemma.\nHere we extend and prove this result, providing pairs ($\\gamma,\\delta$)\nlabelled by the Lie algebra A$_{N-1}$, two non-negative integers $\\ell$ and $k$\nand a partition $\\lambda$, whose parts do not exceed $N-1$. Our results give\nrise to what we call a ``higher-level\u0027\u0027 Bailey lemma. As an application it is\nshown how this lemma can be applied to yield general $q$-series identities,\nwhich generalize some well-known results of Andrews and Bressoud.",
"arxiv_id": "q-alg/9607014",
"authors": [
"Anne Schilling",
"S. Ole Warnaar"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "A Higher-Level Bailey Lemma: Proof and Application",
"url": "https://arxiv.org/abs/q-alg/9607014"
},
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