{"title":"后代彩色琼斯多项式","authors":"Stavros Garoufalidis, Rinat Kashaev","doi":"10.4310/pamq.2023.v19.n5.a2","DOIUrl":null,"url":null,"abstract":"We discuss two realizations of the colored Jones polynomials of a knot, one appearing in an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another formulated in terms of a sequence of elements of the Habiro ring appearing in recent work of D. Zagier and the first author on the Refined Quantum Modularity Conjecture.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"24 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The descendant colored Jones polynomials\",\"authors\":\"Stavros Garoufalidis, Rinat Kashaev\",\"doi\":\"10.4310/pamq.2023.v19.n5.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss two realizations of the colored Jones polynomials of a knot, one appearing in an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another formulated in terms of a sequence of elements of the Habiro ring appearing in recent work of D. Zagier and the first author on the Refined Quantum Modularity Conjecture.\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2023.v19.n5.a2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2023.v19.n5.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们讨论了结的彩色琼斯多项式的两种实现方式，一种出现在第二作者 1994 年关于从五边形特性解中获得的统一根量子 R 矩阵的一项未被注意的工作中，另一种则出现在 D. Zagier 和第一作者关于精炼量子模块性猜想的最新工作中，以哈比罗环元素序列的形式制定。
We discuss two realizations of the colored Jones polynomials of a knot, one appearing in an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another formulated in terms of a sequence of elements of the Habiro ring appearing in recent work of D. Zagier and the first author on the Refined Quantum Modularity Conjecture.
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