The $\mathfrak{sl}_3$ colored Jones polynomials for $2$-bridge links

Wataru Yuasa

doi:10.1142/s0218216517500389

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arXiv · 1609.07289

The $\mathfrak{sl}_3$ colored Jones polynomials for $2$-bridge links

Wataru Yuasa

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Abstract

Kuperberg introduced web spaces for some Lie algebras which are generalizations of the Kauffman bracket skein module on a disk with marked points. We derive some formulas for $A_1$ and $A_2$ clasped web spaces by graphical calculus using skein theory. These formulas are colored version of skein relations, twist formulas and bubble skein expansion formulas. We calculate the $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ colored Jones polynomials of $2$-bridge knots and links explicitly using twist formulas.

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BibTeX RIS

Wataru Yuasa. 2016-09-23. The $\mathfrak{sl}_3$ colored Jones polynomials for $2$-bridge links. https://doi.org/10.1142/s0218216517500389

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