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DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

KAZUHIRO HIKAMI

Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7–3–1, Bunkyo, Tokyo 113–0033, Japan

https://doi.org/10.1142/S0129167X04002582Cited by:34 (Source: Crossref)

Abstract

We prove that the N-colored Jones polynomial for the torus knot satisfies the second order difference equation, which reduces to the first order difference equation for a case of . We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for .

Keywords:

AMSC: 57M27, 57M50, 39A70

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