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2012

Knot polynomials in the first non-symmetric representation

Anokhina, A., Mironov, A., Morozov, A. et al.

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We describe the explicit form and the hidden structure of the answer for the HOMFLY polynomial for the figure eight and some other 3-strand knots in representation [21].

This is the first result for non-torus knots beyond (anti)symmetric representations, and its evaluation is far more complicated.
We provide a whole variety of different arguments, allowing one to guess the answer for the figure eight knot, which can be also partly used in more complicated situations.
Finally we report the result of exact calculation for figure eight and some other 3-strand knots based on the previously developed sophisticated technique of multi-strand calculations.

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J.W.Alexander, Trans.Amer.Math.Soc. 30
1987
Earlier work this paper cites.
P.Freyd, D.Yetter, J.Hoste, W.B.R.Lickorish, K.Millet, A.Ocneanu, Bull. AMS. 12
1987
Earlier work this paper cites.
E.Witten, Comm.Math.Phys. 121
1989
Earlier work this paper cites.
E.Guadagnini, M.Martellini and M.Mintchev, In Clausthal 1989, Proceedings, Quantum groups, 307-317; Phys.Lett. B235 (1990) 275; N.Yu.Reshetikhin and V.G.Turaev, Comm. Math. Phys. 127
1990
Earlier work this paper cites.

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