A motivated proof of the Göllnitz–Gordon–Andrews identities

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• 作者：Bud Coulson ; Shashank Kanade ; James Lepowsky ; Robert McRae ; Fei Qi…
• 关键词：Göllnitz–Gordon–Andrews identities ; Partition identities ; Vertex operator algebras
• 刊名：The Ramanujan Journal
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：42
• 期：1
• 页码：97-129
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Number Theory; Field Theory and Polynomials; Combinatorics; Fourier Analysis; Functions of a Complex Variable;
• 出版者：Springer US
• ISSN：1572-9303
• 卷排序：42

文摘

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.