Colored knot polynomials for arbitrary pretzel knots and links
A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SU _{N}), and looks related to a modular transformation of toric conformal block. Knot polynomials are among the hottest topics in modern theory. They are supposed to summarize nicely representation theory of quantum algebras and modular properties of conformal blocks. The result reported in the present letter, provides a spectacular illustration and support to this general expectation.
 Authors:

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 ITEP, Moscow (Russia); Rutgers Univ., Piscataway, NJ (United States)
 ITEP, Moscow (Russia); International Institute of Physics, Natal (Brazil)
 Lebedev Physics Institute, Moscow (Russia); ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia)
 ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia)
 ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia); Chelyabinsk State Univ., Chelyabinsk (Russia)
 Publication Date:
 Grant/Contract Number:
 SC0010008; ARRASC0003883; SC0007897
 Type:
 Published Article
 Journal Name:
 Physics Letters. Section B
 Additional Journal Information:
 Journal Volume: 743; Journal Issue: C; Journal ID: ISSN 03702693
 Publisher:
 Elsevier
 Research Org:
 Rutgers Univ., Piscataway, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1198587
 Alternate Identifier(s):
 OSTI ID: 1188772
Galakhov, D., Melnikov, D., Mironov, A., Morozov, A., and Sleptsov, A.. Colored knot polynomials for arbitrary pretzel knots and links. United States: N. p.,
Web. doi:10.1016/j.physletb.2015.02.029.
Galakhov, D., Melnikov, D., Mironov, A., Morozov, A., & Sleptsov, A.. Colored knot polynomials for arbitrary pretzel knots and links. United States. doi:10.1016/j.physletb.2015.02.029.
Galakhov, D., Melnikov, D., Mironov, A., Morozov, A., and Sleptsov, A.. 2015.
"Colored knot polynomials for arbitrary pretzel knots and links". United States.
doi:10.1016/j.physletb.2015.02.029.
@article{osti_1198587,
title = {Colored knot polynomials for arbitrary pretzel knots and links},
author = {Galakhov, D. and Melnikov, D. and Mironov, A. and Morozov, A. and Sleptsov, A.},
abstractNote = {A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SUN), and looks related to a modular transformation of toric conformal block. Knot polynomials are among the hottest topics in modern theory. They are supposed to summarize nicely representation theory of quantum algebras and modular properties of conformal blocks. The result reported in the present letter, provides a spectacular illustration and support to this general expectation.},
doi = {10.1016/j.physletb.2015.02.029},
journal = {Physics Letters. Section B},
number = C,
volume = 743,
place = {United States},
year = {2015},
month = {4}
}