幽灵级数和布列索-哥尼兹-哥顿等式的动机证明

John Layne, Samuel Marshall, Christopher Sadowski, Emily Shambaugh
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摘要

我们提出了对布赖索德-哥尼兹-哥顿等式的 "动机证明"。安德鲁斯和巴克斯特对罗杰斯-拉玛努扬等式以及莱波夫斯基和朱对戈登等式也给出了类似的 "动机证明"。此外,Kanade、Lepowsky、Russell 和 Sills 也给出了安德鲁斯-布雷斯德等式的 "动机证明",Coulson、Kanade、Lepowsky、McRae、Qi、Russell 和第三位作者也给出了戈尔诺-戈登-安德鲁斯等式的 "动机证明"。我们的证明既借鉴了安德鲁-布雷斯德等式 "动机证明 "中 "幽灵级数 "的使用,也使用了与哥尼兹-哥顿-安德鲁等式 "动机证明 "中类似的递推。我们预计布雷斯德-戈尔尼茨-戈登等式的 "动机证明 "将阐明某些扭曲顶点代数构造。
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Ghost series and a motivated proof of the Bressoud–Göllnitz–Gordon identities

We present what we call a “motivated proof” of the Bressoud-Göllnitz-Gordon identities. Similar “motivated proofs” have been given by Andrews and Baxter for the Rogers–Ramanujan identities and by Lepowsky and Zhu for Gordon’s identities. Additionally, “motivated proofs” have also been given for the Andrews-Bressoud identities by Kanade, Lepowsky, Russell, and Sills and for the Göllnitz–Gordon–Andrews identities by Coulson, Kanade, Lepowsky, McRae, Qi, Russell, and the third author. Our proof borrows both the use of “ghost series” from the “motivated proof” of the Andrews–Bressoud identities and uses recursions similar to those found in the “motivated proof” of the Göllnitz–Gordon–Andrews identities. We anticipate that this “motivated proof” of the Bressoud–Göllnitz–Gordon identities will illuminate certain twisted vertex-algebraic constructions.

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