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arXiv · 1207.0279

Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids

A. Anokhina·A. Mironov·A. Morozov·An. Morozov
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Abstract

Basing on evaluation of the Racah coefficients for SU_q(3) (which supported the earlier conjecture of their universal form) we derive explicit formulas for all the 5-, 6- and 7-strand Wilson averages in the fundamental representation of arbitrary SU(N) group (the HOMFLY polynomials). As an application, we list the answers for all 5-strand knots with 9 crossings. In fact, the 7-strand formulas are sufficient to reproduce all the HOMFLY polynomials from the katlas.org: they are all described at once by a simple explicit formula with a very transparent structure. Moreover, would the formulas for the relevant SU_q(3) Racah coefficients remain true for all other quantum groups, the paper provides a complete description of the fundamental HOMFLY polynomials for all braids with any number of strands.

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A. Anokhina, A. Mironov, A. Morozov, An. Morozov. 2012-10-30. Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids. https://doi.org/10.1016/j.nuclphysb.2012.11.006

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