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."
arXiv comment23 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
References in corpus (10)
- Quasi-particles models for the representations of Lie algebras and geometry of flag manifold
- Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
- Rogers-Schur-Ramanujan type identities for the minimal models of conformal field theory
- Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
- A framework of Rogers-Ramanujan identities and their arithmetic properties
- Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
- Identities of the Rogers--Ramanujan--Slater Type
- A motivated proof of the Göllnitz-Gordon-Andrews identities
- Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E
- Principal subspaces of higher-level standard sl(3)^-modules