统一Witten-Reshetikhin-Turaev不变量族的hecke型公式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-01-01 DOI:10.4310/CNTP.2017.V11.N2.A1

K. Hikami, Jeremy Lovejoy

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引用次数: 6

摘要

每一个闭合的可定向3流形都可以通过在s中的连杆上进行手术来构造。在沿环面结进行手术的情况下，可以得到一个Seifert纤维流形。本文考虑了这类流形的三个族，并研究了它们的统一WittenReshetikhin-Turaev (WRT)不变量。由于最近对(2,2t + 1)-环面结的彩色琼斯多项式的分环展开中的系数的计算，这些WRT不变量可以整齐地表示为收敛于单位圆盘内的q超几何级数。使用Rosso-Jones公式和一些非标准的贝利对技术，我们找到了这些不变量的赫克式公式。我们还评论了它们的模拟和量子模块化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

Every closed orientable 3-manifold can be constructed by surgery on a link in S. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified WittenReshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t+ 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.