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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

DOI: https://doi.org/10.4213/tmf8588

Full text: PDF file (1152 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 178:1, 1–58

Bibliographic databases:

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

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    This publication is cited in the following articles:
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    3. A. Mironov, A. Morozov, A. Morozov, “On colored HOMFLY polynomials for twist knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183  crossref  zmath  adsnasa  isi  scopus
    4. A. Anokhina, A. Morozov, “Towards $\mathscr R$-matrix construction of Khovanov–Rozansky polynomials I: primary $T$-deformation of HOMFLY”, J. High Energy Phys., 2014, no. 7, 063  crossref  mathscinet  zmath  isi  elib  scopus
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    7. JETP Letters, 101:1 (2015), 51–56  mathnet  crossref  crossref  isi  elib  elib
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    9. A. Morozov, A. Morozov, A. Popolitov, “On matrix-model approach to simplified Khovanov–Rozansky calculus”, Phys. Lett. B, 749 (2015), 309–325  crossref  zmath  adsnasa  isi  elib  scopus
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    30. A. Mironov, A. Morozov, “Eigenvalue conjecture and colored Alexander polynomials”, Eur. Phys. J. C, 78:4 (2018), 284  crossref  isi  scopus
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    32. A. Anokhina, A. Morozov, “Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?”, J. High Energy Phys., 2018, no. 4, 066  crossref  mathscinet  isi  scopus
    33. S. Dhara, A. Mironov, A. Morozov, A. Morozov, P. Ramadevi, V. K. Singh, A. Sleptsov, “Eigenvalue hypothesis for multistrand braids”, Phys. Rev. D, 97:12 (2018), 126015  crossref  isi  scopus
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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