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This article is cited in 13 scientific papers (total in 13 papers)
FIELDS, PARTICLES, AND NUCLEI
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.
DOI:
https://doi.org/10.7868/S0370274X13040012
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English version:
Journal of Experimental and Theoretical Physics Letters, 2013, 97:4, 171–172
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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
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Linking options:
http://mi.mathnet.ru/eng/jetpl3350 http://mi.mathnet.ru/eng/jetpl/v97/i4/p195
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. S. Anokhina, A. A. Morozov, “Cabling procedure for the colored HOMFLY polynomials”, Theoret. and Math. Phys., 178:1 (2014), 1–58
    -
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
-
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
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Mironov A. Morozov A. Morozov A., “on Colored Homfly Polynomials For Twist Knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183
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Morozov A., Morozov A., Morozov A., “on Possible Existence of Homfly Polynomials For Virtual Knots”, Phys. Lett. B, 737 (2014), 48–56
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JETP Letters, 101:12 (2015), 831–834
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Kononov Ya., Morozov A., “Factorization of Colored Knot Polynomials At Roots of Unity”, Phys. Lett. B, 747 (2015), 500–510
-
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
-
Mironov A. Morozov A. Sleptsov A., “Colored Homfly Polynomials For the Pretzel Knots and Links”, J. High Energy Phys., 2015, no. 7, 069
-
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
-
Morozov A.A., “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837
-
Morozov A., “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605
-
Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646
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