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New Symmetries for the Uq(slN) 6-j Symbols from the Eigenvalue Conjecture1

  • Methods of Theoretical Physics
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Abstract

In the present paper, we discuss the eigenvalue conjecture, suggested in 2012, in the particular case of Uq(slN) 6-j The eigenvalue conjecture provides a certain symmetry for Racah coefficients and we prove that the eigenvalue conjecture is provided by the Regge symmetry for Uq(slN) 6-j, when three representations coincide. This in perspective provides us a kind of generalization of the Regge symmetry to arbitrary Uq(slN) 6-j.

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References

  1. A. Kirillov and N. Reshetikhin, in New Developments in the Theory of Knots (World Scientific, Singapore, 1990), p. 202.

    Book  Google Scholar 

  2. S. Nawata, P. Ramadevi, and Zodinmawia, Lett. Math. Phys. 103, 1389 (2013); arXiv:1302.5143.

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Nawata, P. Ramadevi, and Zodinmawia, J. Knot Theory Ramific. 22, 13 (2013); arXiv:1302.5144.

    Article  Google Scholar 

  4. A. Mironov, A. Morozov, and A. Sleptsov, J. High Energy Phys. 07, 069 (2015); arXiv:1412.8432.

    Article  ADS  Google Scholar 

  5. A. Caudron, Publ. Math. Orsay No. 82-4 (Univ. Paris XI, Orsay, 1982).

    Google Scholar 

  6. F. Bonahon and L. C. Siebenmann, http://wwwbcf. usc.edu/~fbonahon/Research/Preprints/Bon-Sieb.pdf (2010).

    Google Scholar 

  7. P. Ramadevi, T. R. Govindarajan, and R. K. Kaul, Mod. Phys. Lett. A 9, 3205 (1994); hep-th/9401095.

    Article  ADS  Google Scholar 

  8. D. Galakhov, D. Melnikov, A. Mironov, A. Morozov, and A. Sleptsov, Phys. Lett. B 743, 71 (2015); arXiv:1412.2616.

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, and V. K. Singh, J. High Energy Phys. 1507, 109 (2015); arXiv:1504.00371.

    Article  ADS  Google Scholar 

  10. R. K. Kaul and T. R. Govindarajan, Nucl. Phys. B 380, 293 (1992); hep-th/9111063.

    Article  ADS  Google Scholar 

  11. P. Ramadevi, T. R. Govindarajan, and R. K. Kaul, Nucl. Phys. B 402, 548 (1993); hep-th/9212110.

    Article  ADS  Google Scholar 

  12. P. Ramadevi, T. R. Govindarajan, and R. K. Kaul, Nucl. Phys. B 422, 291 (1994); hep-th/9312215.

    Article  ADS  Google Scholar 

  13. P. Ramadevi and T. Sarkar, Nucl. Phys. B 600, 487 (2001); hep-th/0009188.

    Article  ADS  Google Scholar 

  14. J. Gu and H. Jockers, Comm. Math. Phys. 338, 393 (2015); arXiv: 1407.5643.

    Article  ADS  MathSciNet  Google Scholar 

  15. A. Mironov, A. Morozov, and An. Morozov, J. High Energy Phys. 03, 034 (2012); arXiv:1112.2654.

    Article  ADS  Google Scholar 

  16. H. Itoyama, A. Mironov, A. Morozov, and An. Morozov, Int. J. Mod. Phys. A 28, 1340009 (2013); arXiv:1209.6304.

    Article  ADS  Google Scholar 

  17. I. Tuba and H. Wenzl, Pacif. J. Math. 197, 491510 (2001); arXiv:math/9912013.

    Article  Google Scholar 

  18. A. Mironov and A. Morozov, Phys. Lett. B 755 (10), 47 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  19. S. Dhara, A. Mironov, A. Morozov, An. Morozov, P.Ramadevi, V. K. Singh, and A. Sleptsov, arXiv:1805.03916.

  20. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Pergamon, Oxford, 1977; Nauka, Moscow, 1989).

    Google Scholar 

  21. M. Rosso and V. F. R. Jones, J. Knot Theory Ramific. 2, 97 (1993).

    Article  Google Scholar 

  22. E. Guadagnini, M. Martellini, and M. Mintchev, Lect. Notes Phys. 370, 307 (1990).

    Article  ADS  Google Scholar 

  23. E. Guadagnini, M. Martellini, and M. Mintchev, Phys. Lett. B 235, 275 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  24. N. Yu. Reshetikhin and V. G. Turaev, Comm. Math. Phys. 127, 1 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  25. K. Liu and P. Peng, J. Differ. Geom. 85, 479 (2010); arXiv:0704.1526.

    Article  Google Scholar 

  26. A. Klimyk and K. Schmüdgen, Quantum Groups and Their Representations (Springer Science, New York, 2012).

    MATH  Google Scholar 

  27. X.-S. Lin and H. Zheng, Trans. Am. Math. Soc. 362, 1 (2010); math/0601267.

    Article  Google Scholar 

  28. A. Mironov, A. Morozov, An. Morozov, and A. Sleptsov, J. Mod. Phys. A 30, 1550169 (2015); arXiv:1508.02870.

    Article  ADS  Google Scholar 

  29. A. Mironov, A. Morozov, An. Morozov, and A. Sleptsov, J. High Energy Phys. 2016, 134 (2016); arXiv:1605.02313.

    Article  Google Scholar 

  30. A. Mironov, A. Morozov, An. Morozov, and A. Sleptsov, JETP Lett. 104, 56 (2016); arXiv:1605.03098.

    Article  ADS  Google Scholar 

  31. Sh. Shakirov and A. Sleptsov, arXiv:1611.03797.

  32. C. Bai, J. Jiang, J. Liang, A. Mironov, A. Morozov, An. Morozov, and A. Sleptsov, J. Geom. Phys. 132, 155 (2018); arXiv:1801.09363.

    Article  ADS  MathSciNet  Google Scholar 

  33. M. Gould and Y. Zhang, J. Math. Phys. 35, 6757 (1994); arXiv: hep-th/9311041.

    Article  ADS  MathSciNet  Google Scholar 

  34. C. R. Lienert and P. H. Butler, J. Phys. A: Math. Gen. 25, 1223 (1992).

    Article  ADS  Google Scholar 

  35. F. Pan, J. Phys. A: Math. Gen. 26, 4621 (1993).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow region, 141701, Russia

    A. Morozov & A. Sleptsov

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127994, Russia

    A. Morozov & A. Sleptsov

  3. Institute for Theoretical and Experimental Physics, Moscow, 117218, Russia

    A. Morozov & A. Sleptsov

  4. Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk, 454001, Russia

    A. Sleptsov

Authors
  1. A. Morozov
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  2. A. Sleptsov
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Correspondence to A. Sleptsov.

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Morozov, A., Sleptsov, A. New Symmetries for the Uq(slN) 6-j Symbols from the Eigenvalue Conjecture1. Jetp Lett. 108, 697–704 (2018). https://doi.org/10.1134/S0021364018220058

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  • DOI: https://doi.org/10.1134/S0021364018220058

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