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Pis'ma v Zh. Èksper. Teoret. Fiz., 2013, Volume 97, Issue 4, Pages 195–196 (Mi jetpl3350)  

This article is cited in 13 scientific papers (total in 13 papers)


The first-order deviation of superpolynomial in an arbitrary representation from the special polynomial

A. Morozov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow

Abstract: Like all other knot polynomials, the superpolynomials should be defined in arbitrary representation $R$ of the gauge group in (refined) Chern–Simons theory. However, not a single example is yet known of a superpolynomial beyond symmetric or antisymmetric representations. Following the article Equations on knot polynomials and 3d/5d duality, we consider the expansion of the superpolynomial around the special polynomial in powers of $q-1$ and $t-1$ and suggest a simple formula for the first-order deviation, which is presumably valid for arbitrary representation. This formula can serve as a crucial lacking test of various formulas for non-trivial superpolynomials, which will appear in the literature in the near future.


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English version:
Journal of Experimental and Theoretical Physics Letters, 2013, 97:4, 171–172

Bibliographic databases:

Document Type: Article
Received: 22.11.2012
Revised: 25.01.2013
Language: English

Citation: A. Morozov, “The first-order deviation of superpolynomial in an arbitrary representation from the special polynomial”, Pis'ma v Zh. Èksper. Teoret. Fiz., 97:4 (2013), 195–196; JETP Letters, 97:4 (2013), 171–172

Citation in format AMSBIB
\by A.~Morozov
\paper The first-order deviation of superpolynomial
in an arbitrary representation from the special polynomial
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2013
\vol 97
\issue 4
\pages 195--196
\jour JETP Letters
\yr 2013
\vol 97
\issue 4
\pages 171--172

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    This publication is cited in the following articles:
    1. A. S. Anokhina, A. A. Morozov, “Cabling procedure for the colored HOMFLY polynomials”, Theoret. and Math. Phys., 178:1 (2014), 1–58  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. B. Arthamonov, A. D. Mironov, A. Yu. Morozov, “Differential hierarchy and additional grading of knot polynomials”, Theoret. and Math. Phys., 179:2 (2014), 509–542  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Anokhina A. Morozov A., “Towards 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
    4. Mironov A. Morozov A. Morozov A., “on Colored Homfly Polynomials For Twist Knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183  crossref  zmath  adsnasa  isi  elib  scopus
    5. Morozov A., Morozov A., Morozov A., “on Possible Existence of Homfly Polynomials For Virtual Knots”, Phys. Lett. B, 737 (2014), 48–56  crossref  zmath  adsnasa  isi  elib  scopus
    6. JETP Letters, 101:12 (2015), 831–834  mathnet  crossref  crossref  isi  elib  elib
    7. Kononov Ya., Morozov A., “Factorization of Colored Knot Polynomials At Roots of Unity”, Phys. Lett. B, 747 (2015), 500–510  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Mironov A., Morozov A., Morozov A., Ramadevi P., Singh V.K., “Colored Homfly Polynomials of Knots Presented as Double Fat Diagrams”, J. High Energy Phys., 2015, no. 7, 109  crossref  mathscinet  isi  scopus
    9. Mironov A. Morozov A. Sleptsov A., “Colored Homfly Polynomials For the Pretzel Knots and Links”, J. High Energy Phys., 2015, no. 7, 069  crossref  mathscinet  isi  scopus
    10. Mironov A. Morozov A. Morozov A. Sleptsov A., “HOMFLY polynomials in representation [3, 1] for 3-strand braids”, J. High Energy Phys., 2016, no. 9, 134  crossref  mathscinet  zmath  isi  scopus
    11. Morozov A.A., “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837  crossref  isi  elib  scopus
    12. Morozov A., “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605  crossref  zmath  isi  elib  scopus
    13. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
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