Ghost series and a motivated proof of the Andrews-Bressoud identities
arXiv:1411.2048 · doi:10.1016/j.jcta.2016.07.004
Abstract
We present what we call a "motivated proof" of the Andrews-Bressoud partition identities for even moduli. A "motivated proof" of the Rogers-Ramanujan identities was given by G. E. Andrews and R. J. Baxter, and this proof was generalized to the odd-moduli case of Gordon's identities by J. Lepowsky and M. Zhu. Recently, a "motivated proof" of the somewhat analogous Göllnitz-Gordon-Andrews identities has been found. In the present work, we introduce "shelves" of formal series incorporating what we call "ghost series," which allow us to pass from one shelf to the next via natural recursions, leading to our motivated proof. We anticipate that these new series will provide insight into the ongoing program of vertex-algebraic categorification of the various "motivated proofs."
23 pages. This paper continues the "motivated proof" program developed in earlier work of J. Lepowsky and M. Zhu [arXiv:1205.6570] and of B. Coulson, S. Kanade, J. Lepowsky, R. McRae, F. Qi, M. C. Russell and C. Sadowski [arXiv:1411.2044]. Mention of further work is added
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