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TMF, 2014, Volume 178, Number 1, Pages 3–68 (Mi tmf8588)  

This article is cited in 37 scientific papers (total in 37 papers)

Cabling procedure for the colored HOMFLY polynomials

A. S. Anokhinaab, A. A. Morozovca

a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
c Lomonosov Moscow State University, Moscow, Russia

Abstract: We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We describe how it can be used and how the projectors and $\mathcal R$-matrices needed for this procedure can be found. The constructed matrix expressions for the projectors and $\mathcal R$-matrices in the fundamental representation allow calculating the HOMFLY polynomial in an arbitrary representation for an arbitrary knot. The computational algorithm can be used for the knots and links with $|Q|m\le12$, where $m$ is the number of strands in a braid representation of the knot and $|Q|$ is the number of boxes in the Young diagram of the representation. We also discuss the justification of the cabling procedure from the group theory standpoint, deriving expressions for the fundamental $\mathcal R$-matrices and clarifying some conjectures formulated in previous papers.

Keywords: Chern–Simons theory, knot theory, representation theory


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Theoretical and Mathematical Physics, 2014, 178:1, 1–58

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Document Type: Article
Received: 27.08.2013

Citation: A. S. Anokhina, A. A. Morozov, “Cabling procedure for the colored HOMFLY polynomials”, TMF, 178:1 (2014), 3–68; Theoret. and Math. Phys., 178:1 (2014), 1–58

Citation in format AMSBIB
\by A.~S.~Anokhina, A.~A.~Morozov
\paper Cabling procedure for the~colored HOMFLY polynomials
\jour TMF
\yr 2014
\vol 178
\issue 1
\pages 3--68
\jour Theoret. and Math. Phys.
\yr 2014
\vol 178
\issue 1
\pages 1--58

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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