Quantum Racah matrices and 3-strand braids in representation [3,3]

Shakirov, Sh.; Слепцов, А.

doi:10.1016/j.geomphys.2021.104273

Cited by 3 publications

(3 citation statements)

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“…• For 3-strand knots, there are explicit formulas for R-matrices for representations R = [r], [2,1], [2,2], [3,3] [ [53][54][55][56][57], which allow one to compute corresponding HOMFLY polynomials.…”

Section: Group Factors Associated With Jacobi Diagramsmentioning

confidence: 99%

“…• For arborescent knots, the same information for the same representations are given in [57][58][59][60][61]. Reference [62] can be useful for detailed information on arborescent calculus with explicit examples.…”

Section: Group Factors Associated With Jacobi Diagramsmentioning

confidence: 99%

“…• The representation R = [4, 1] for 3-strand knots were calculated by the same method given in [57]. The answer can be found on the cite [51] in Section DATA: Racah.…”

Section: Group Factors Associated With Jacobi Diagramsmentioning

confidence: 99%

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Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure

Lanina,

Sleptsov,

Tselousov

2021

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We have recently proposed [1] a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with SU (N ) gauge group. In this paper, we apply the developed method to obtain and study various properties, including nonperturbative ones, of such vacuum expectation values.First, we discuss the computation of Vassiliev invariants. Second, we discuss the Vogel theorem of not distinguishing chord diagrams by weight systems coming from semisimple Lie (super)algebras. Third, we provide a method for constructing linear recursive relations for the colored Jones polynomials considering a special case of torus knots T [2, 2k + 1]. Fourth, we give a generalization of the one-hook scaling property for the colored Alexander polynomials. And finally, for the group factors we provide a combinatorial description, which has a clear dependence on the rank N and the representation R.

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