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

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

Bibliographic databases:

Document Type: Article
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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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. Mironov A. Morozov A. Morozov A., “on Colored Homfly Polynomials For Twist Knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183
5. Morozov A., Morozov A., Morozov A., “on Possible Existence of Homfly Polynomials For Virtual Knots”, Phys. Lett. B, 737 (2014), 48–56
6. JETP Letters, 101:12 (2015), 831–834
7. Kononov Ya., Morozov A., “Factorization of Colored Knot Polynomials At Roots of Unity”, Phys. Lett. B, 747 (2015), 500–510
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
9. Mironov A. Morozov A. Sleptsov A., “Colored Homfly Polynomials For the Pretzel Knots and Links”, J. High Energy Phys., 2015, no. 7, 069
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
11. Morozov A.A., “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837
12. Morozov A., “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605
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
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