A motivated proof of the Göllnitz-Gordon-Andrews identities

Abstract

We present what we call a "motivated proof" of the Göllnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the Göllnitz-Gordon-Andrews identities will illuminate certain twisted vertex-algebraic constructions.

27 pages. This paper includes appendices supplementing ideas in an earlier paper of J. Lepowsky and M. Zhu [arXiv:1205.6570]. Mention of further work is added