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