A Higher-Level Bailey Lemma: Proof and Application

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.

Latex2e, 21 pages, 1 Postscript figure. Several typos have been corrected including a serious one, a figure has been added and the discussion has been improved. Version to appear in the Ramanujan Journal

References in corpus (5)

• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)
• A Higher-level Bailey Lemma
• N=2 Supersymmetry and Bailey Pairs
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Cited by in corpus (2)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$