Multistrand Eigenvalue Conjecture and Racah Symmetries
- Authors: Morozov A.1,2
-
Affiliations:
- National Research Center Kurchatov Institute
- Institute for Information Transition Problems
- Issue: Vol 117, No 3-4 (2) (2023)
- Pages: 242-247
- Section: Articles
- URL: https://rjsvd.com/0370-274X/article/view/663517
- DOI: https://doi.org/10.31857/S1234567823030102
- EDN: https://elibrary.ru/OXRSBG
- ID: 663517
Cite item
Abstract
Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with
matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue conjecture. In this paper we study symmetries of Racah matrices which follow from the eigenvalue conjecture for multistrand braids.
About the authors
An. Morozov
National Research Center Kurchatov Institute; Institute for Information Transition Problems
Author for correspondence.
Email: morozov.andrey.a@iitp.ru
123182, Moscow, Russia; 127051, Moscow, Russia
References
- L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, London, Paris (1997).
- A.Klimyk and K. Schmudgen, Quantum Groups and Their Representations, Springer, Berlin Heidelberg (2012).
- D. Bernard and O. Babelon, Phys. Lett. B 375, 89 (1996); arXiv:q-alg/9511019.
- R. Gambini, J. M. Aroca, and H. Fort, Phys. Rev. D 58, 045007 (1998); arXiv:1407.5643.
- E.R. Livine, Ann. Henri Poincare 18, 1465 (2017); arXiv:1610.02716.
- N.Yu. Reshetikhin and V.G. Turaev, Commun. Math. Phys. 127, 1 (1990).
- V.G. Turaev and O.Ya. Viro, Topology 31, 865 (1992).
- V.G. Turaev, Quantum invariants of knots and 3-manifolds, in De Gruyter Studies in Mathematics, De Gruyter, Berlin, Boston (1994).
- R.K. Kaul, P. Ramadevi, and T.R. Govindarajan, Nucl. Phys. B 402, 548 (1993); arXiv:hep-th/9212110.
- H. Jockers and J. Gu, Commun. Math. Phys. 338, 393 (2015); arXiv:1407.5643.
- A.N. Kirillov and N.Yu. Reshetikhin, Representations of the algebra Uq(sl2), q-orthogonal polynomials and invariants of links, in New Developments in the Theory of Knots. Advanced Series in Mathematical Physics, World Scietific Publishings Co. Pte. Ltd., Singapore (1990), v. 11, p. 202.
- S. Nawata, P. Ramadevi, and Zodinmawia, Lett. Math. Phys. 103, 1389 (2013); arXiv:1302.5143.
- V. Alekseev, An. Morozov, and A. Sleptsov, Nucl. Phys. B 960, 115164 (2020); arXiv:1912.13325.
- H. Itoyama, A. Mironov, A. Morozov, and An. Morozov, Int. J. Mod. Phys. A 28, 1340009 (2013); arXiv:1209.6304.
- A. Mironov and A. Morozov, Eur. Phys. J. C 78(4), 284 (2018); arXiv:1610.03043.
- A. Anokhina and An. Morozov, Teor. Mat. Fiz. 178, 3 (2014); arXiv:1307.2216.
- An.Morozov and A. Sleptsov, Pis'ma v ZhETF 108(10), 721 (2018); arXiv:1905.01876.
- V. Alekseev, An. Morozov, and A. Sleptsov, Lett. Math. Phys. 111, 50 (2021); arXiv:1909.07601.
- S. Dhara, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, V.K. Singh, and A. Sleptsov, Phys. Rev. D 97, 126015 (2018); arXiv:1805.03916.
- V. Mishnyakov, A. Sleptsov, and N. Tselousov, Ann. Henri Poincare 22, 1235 (2021); arXiv:2001.10596.
- V. Mishnyakov, A. Sleptsov, and N. Tselousov, Commun. Math. Phys. 384, 955 (2021); arXiv:2005.01188.
- E. Lanina, A. Sleptsov, and N. Tselousov, Phys. Lett. B 823, 136727 (2021); arXiv:2105.11565.
- E. Lanina and A. Sleptsov, arXiv:2210.07874.
- S. Dhara, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, V.K. Singh, and A. Sleptsov, Phys. Rev. D 97, 126015 (2018); arXiv:1711.10952.
- V.G. Turaev, Invent. Math. 92, 527 (1988).
- N.Yu. Reshetikhin and V.G. Turaev, Commun. Math. Phys. 127, 1 (1990).
- N. Reshetikhin and V.G. Turaev, Invent. Math. 103, 547 (1991).
- A. Morozov and A. Smirnov, Nucl. Phys. B 835, 284 (2010); arXiv:1001.2003.
- A. Smirnov, Notes on Chern-Simons Theory in the Temporal Gauge, The Subnuclear Series, The Most Unexpected at LHC and the Status of High Energy Frontier, Proceedings of the International School of Subnuclear Physics, Erice, Sicily, Italy (2011), v. 47, p. 489; arXiv:0910.5011.
- A. Mironov, A. Morozov, and An. Morozov, JHEP 03, 034 (2012); arXiv:1112.2654.
- M.D. Gould, Lett. Math. Phys. 24(3), 183 (1992).
- N.Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links I, II, LOMI-E-87-4, LOMI-E-87-17 (1998).
- A. Mironov, A. Morozov, and An. Morozov, Character expansion for HOMFLY polynomials. I. Integrability and difference equations, ed. by A. Rebhan, L. Katzarkov, J. Knapp, R. Rashkov, and E. Scheidegger, Strings, gauge fields, and the geometry behind: The legacy of Maximilian Kreuzer, World Scietific Publishins Co. Pte. Ltd., Singapore (2013), p. 101; arXiv:1112.5754.
- L. Bishler, An. Morozov, A. Sleptsov, and Sh. Shakirov, Int. J. Mod. Phys. A 33(17), 1850105 (2018); arXiv:1712.07034.
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