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A 𝑞-SERIES IDENTITY VIA THE 𝔰𝔩₃ COLORED JONES POLYNOMIALS FOR THE (2, 2𝑚)-TORUS LINK
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Journal Article
A 𝑞-SERIES IDENTITY VIA THE 𝔰𝔩₃ COLORED JONES POLYNOMIALS FOR THE (2, 2𝑚)-TORUS LINK
2018
Overview
The colored Jones polynomial is a 𝑞-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A 𝑞-series called a tail is obtained as the limit of the 𝔰𝔩₂ colored Jones polynomials {𝐽𝑛(𝐾; 𝑞)}𝑛 for some link 𝐾, for example, an alternating link. For the 𝔰𝔩₃ colored Jones polynomials, the existence of a tail is unknown. We give two explicit formulas of the tail of the 𝔰𝔩₃ colored Jones polynomials colored by (𝑛, 0) for the (2, 2𝑚)-torus link. These two expressions of the tail provide an identity of 𝑞-series. This is a knot-theoretical generalization of the Andrews–Gordon identities for the Ramanujan false theta function.
Publisher
American Mathematical Society
Subject
