Colored knot polynomials for Pretzel knots and links of arbitrary genus

D. Galakhov; D. Melnikov; A. Mironov; A. Morozov; A. Sleptsov

doi:10.1016/j.physletb.2015.02.029

Colored knot polynomials for Pretzel knots and links of arbitrary genus

High Energy Physics - Theory 2015-03-03 v1 Geometric Topology Quantum Algebra

Authors: D. Galakhov , D. Melnikov , A. Mironov , A. Morozov , A. Sleptsov

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Abstract

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich $(g+1)$ -parametric family of Pretzel knots and links. The answer for the Jones and HOMFLY polynomials is fully and explicitly expressed through the Racah matrix of U_q(SU_N), and looks related to a modular transformation of toric conformal block.

Keywords

colored knot polynomial Pretzel knot Jones polynomial HOMFLY polynomial Racah matrix toric conformal block

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@article{arxiv.1412.2616,
  title  = {Colored knot polynomials for Pretzel knots and links of arbitrary genus},
  author = {D. Galakhov and D. Melnikov and A. Mironov and A. Morozov and A. Sleptsov},
  journal= {arXiv preprint arXiv:1412.2616},
  year   = {2015}
}

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5 pages

Colored knot polynomials for Pretzel knots and links of arbitrary genus

Abstract

Keywords

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