A Higher-level Bailey Lemma

Abstract

We propose a generalization of Bailey's lemma, useful for proving $q$-series identities. As an application, generalizations of Euler's identity, the Rogers-Ramanujan identities, and the Andrews-Gordon identities are derived. This generalized Bailey lemma also allows one to derive identities for the branching functions of higher-level $A_1^{(1)}$ cosets.

Latex, 7 pages, to be published in Int. J. of Mod. Phys. B as the proceedings of the symposium''Exactly soluable models in Statistical Mechanics'', March 1996, Northeastern University, Boston; references added

References in corpus (3)

• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• Virasoro character identities from the Andrews--Bailey construction
• N=2 Supersymmetry and Bailey Pairs

Cited by in corpus (7)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$
• Supernomial coefficients, polynomial identities and $q$-series
• Conjugate Bailey pairs
• A Higher-Level Bailey Lemma: Proof and Application
• Bailey Type Transforms and Applications
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$