Racah matrices and hidden integrability in evolution of knots

We construct a general procedure to extract the exclusive Racah matrices S and S¯ from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R=[1], [2], [3] and [2,2]. The matrices S and S¯ relate respectively the maps (R⊗R)⊗R¯⟶R with R⊗(R⊗R¯...

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Bibliographic Details
Published in:Physics letters. B 2016-09, Vol.760 (C), p.45-58
Main Authors: Mironov, A., Morozov, A., Morozov, An, Sleptsov, A.
Format: Article
Language:English
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Summary:We construct a general procedure to extract the exclusive Racah matrices S and S¯ from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R=[1], [2], [3] and [2,2]. The matrices S and S¯ relate respectively the maps (R⊗R)⊗R¯⟶R with R⊗(R⊗R¯)⟶R and (R⊗R¯)⊗R⟶R with R⊗(R¯⊗R)⟶R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2016.06.041