On Hopf-induced Deformation of Topological Locus

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Abstract

We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations associated with the two components of the link. Most important, we extend the description of this locus to conjugate and, generically, to composite representations and also define the “adjoint” Schur functions emerging in the dual description.

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References

  1. 1.
    S. Gukov, A. Iqbal, C. Kozcaz, and C. Vafa, Commun. Math. Phys. 298, 757 (2010)ADSCrossRefGoogle Scholar
  2. 1a.
    H. Awata and H. Kanno, Int. J. Mod. Phys. A 24, 2253 (2009)ADSCrossRefGoogle Scholar
  3. 1b.
    H. Awata, et al., On topological vertex, tangle calculus and the theory of Hopf polynomials, to appear.Google Scholar
  4. 2.
    P. K. Aravind, Y. Aharonov, and L. Vaidman, in: Potentiality, Entanglement and Passion-at-a-Distance, ed. by R. S. Cohen, M. l Horne, and J. Stachel, Springer, Netherlands (1997), p. 53Google Scholar
  5. 2a.
    L. Kauffman and S. Lomonaco, New J. Phys. 4, 73 (2002)ADSCrossRefGoogle Scholar
  6. 2b.
    L. Kauffman and S. Lomonaco, New J. Phys. 6, 134 (2004)ADSCrossRefGoogle Scholar
  7. 2c.
    V. Balasubramanian, J. R. Fliss, R.G. Leigh, and O. Parrikar, JHEP 2017, 61 (2017)CrossRefGoogle Scholar
  8. 2d.
    V. Balasubramanian, M. De-Cross, J. Fliss, A. Kar, R. G. Leigh, and O. Parrikar, arXiv:1801.01131Google Scholar
  9. 2e.
    D. Melnikov, A. Mironov, S. Mironov, A. Morozov, and An. Morozov, Nucl. Phys. B 926, 491 (2018).ADSCrossRefGoogle Scholar
  10. 3.
    P. Freyd, D. Yetter, J. Hoste, W. B.R. Lickorish, K. Millet, ans A. Ocneanu, Bulletin (New Series) of the American Mathematical Society 12, 239 (1985).CrossRefGoogle Scholar
  11. 3a.
    J.H. Przytycki and K.P. Traczyk, Kobe J. Math. 4, 115 (1987).Google Scholar
  12. 4.
    A. Mironov, R. Mkrtchyan, and A. Morozov, HEP, 02, 78 (2016)ADSGoogle Scholar
  13. 4a.
    A. Mironov and A. Morozov, Phys. Lett. B 755, 47 (2016).ADSMathSciNetCrossRefGoogle Scholar
  14. 5.
    M. Rosso, V.F.R. Jones, and J. Knot, Theory Ramifications 2, 97 (1993)CrossRefGoogle Scholar
  15. 5a.
    X.-S. Lin and H. Zheng, Trans. Amer. Math. Soc. 362, 1 (2010).MathSciNetCrossRefGoogle Scholar
  16. 6.
    A. Mironov, A. Morozov, and S. Natanzon, Theor. Math. Phys. 166, 1 (2011); J. Geom. Physi. 62, 148 (2012).CrossRefGoogle Scholar
  17. 7.
    P. Dunin-Barkowski, A. Mironov, A. Morozov, A. Sleptsov, and A. Smirnov, JHEP 03, 021 (2013)ADSCrossRefGoogle Scholar
  18. 7a.
    A. Mironov, A. Morozovm and An. Morozov, Strings, Gauge Fields, and the Geometry Behind: The Legacy of Maximilian Kreuzer, World Scietific Publishing Co. Pte. Ltd. (2013), p. 101Google Scholar
  19. 7b.
    A. Mironov, A. Morozov, and An. Morozov, JHEP 03, 034 (2012).ADSCrossRefGoogle Scholar
  20. 8.
    A. Mironov, A. Morozov, and An. Morozov, arXiv:1804.07278.Google Scholar
  21. 9.
    H.R. Morton and S.G. Lukac, J. Knot Theory Ramifications 12, 395 (2003).MathSciNetCrossRefGoogle Scholar
  22. 10.
    M. Mari no, Rev. Mod. Phys. 77, 675 (2005).ADSCrossRefGoogle Scholar
  23. 11.
    M. Atiyah, Topology 29, 1 (1990).MathSciNetCrossRefGoogle Scholar
  24. 12.
    M. Mari no and C. Vafa, Contemp. Math. 310, 185 (2002)CrossRefGoogle Scholar
  25. 12a.
    M. Mari no, Enumerative geometry and knot invariants, in: 70-th Meeting between Physicists, Theorist and Mathematicians, Strasbourg, France, May 23-25 (2002).Google Scholar
  26. 13.
    C. Bai, J. Jiang, J. Liang, A. Mironov, A. Morozov, An. Morozov, and A. Sleptsov, Phys. Lett. B 778, 197 (2018).ADSCrossRefGoogle Scholar
  27. 14.
    M. Aganagic, T. Ekholm, L. Ng, and C. Vafa, Adv. Theor. Math. Phys. 18, 827 (2014).MathSciNetCrossRefGoogle Scholar
  28. 15.
    S. Arthamonov, A. Mironov, A. Morozov, and An. Morozov, JHEP 04, 156 (2014).ADSCrossRefGoogle Scholar
  29. 16.
    K. Koike, Adv. Math. 74, 57 (1989).MathSciNetCrossRefGoogle Scholar
  30. 17.
    H. Kanno, Nucl. Phys. B 745, 165 (2006).ADSCrossRefGoogle Scholar
  31. 18.
    M. Aganagic, A. Neitzke, and C. Vafa, Adv. Theor. Math. Phys. 10, 603 (2006).MathSciNetCrossRefGoogle Scholar
  32. 19.
    D. J. Gross and W. Taylor, Nucl. Phys. B 400, 181 (1993).ADSCrossRefGoogle Scholar
  33. 20.
    M. Mari no, Commun. Math. Phys. 298, 613 (2010).ADSCrossRefGoogle Scholar

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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Lebedev Physics InstituteMoscowRussia
  2. 2.Institute for Theoretical and Experimental PhysicsMoscowRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia

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