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Pis'ma v Zh. Èksper. Teoret. Fiz., 2016, Volume 104, Issue 1, Pages 52–57 (Mi jetpl5007)  

This article is cited in 13 scientific papers (total in 13 papers)


Quantum Racah matrices and 3-strand braids in irreps $R$ with $|R|=4$

A. Mironovabcd, A. Morozovbcd, An. Morozovecd, A. Sleptsovebcd

a Lebedev Physics Institute, Moscow, Russia
b Institute of Theoretical and Experimental Physics, Moscow, Russia
c Institute for Information Transmission Problems, Moscow, Russia
d National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia
e Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk, Russia

Abstract: We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation $R=[2,2]$ for quantum groups $U_q(sl_N)$. Most of them have sizes $2$, $3$, and $4$ and are fully described by the eigenvalue hypothesis. Of two $6 \times 6$ matrices, one is also described in this way, but the other one corresponds to the case of degenerate eigenvalues and is evaluated by the highest weight method. Together with the much harder calculation for $R=[3,1]$ and with the new method to extract exclusive matrices $J$ and $\overline{J}$ from the inclusive ones, this completes the story of Racah matrices for $|R|\leqslant4$ and allows one to calculate and investigate the corresponding colored HOMFLY polynomials for arbitrary $3$-strand and arborescent knots.

Funding Agency Grant Number
Russian Science Foundation 16-11-10291


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English version:
Journal of Experimental and Theoretical Physics Letters, 2016, 104:1, 56–61

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Document Type: Article
Received: 24.05.2016

Citation: A. Mironov, A. Morozov, An. Morozov, A. Sleptsov, “Quantum Racah matrices and 3-strand braids in irreps $R$ with $|R|=4$”, Pis'ma v Zh. Èksper. Teoret. Fiz., 104:1 (2016), 52–57; JETP Letters, 104:1 (2016), 56–61

Citation in format AMSBIB
\by A.~Mironov, A.~Morozov, An.~Morozov, A.~Sleptsov
\paper Quantum Racah matrices and 3-strand braids in irreps $R$ with $|R|=4$
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2016
\vol 104
\issue 1
\pages 52--57
\jour JETP Letters
\yr 2016
\vol 104
\issue 1
\pages 56--61

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    This publication is cited in the following articles:
    1. Kononov Ya. Morozov A., “On rectangular HOMFLY for twist knots”, Mod. Phys. Lett. A, 31:38 (2016), 1650223  crossref  mathscinet  zmath  isi  elib  scopus
    2. Morozov A., “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605  crossref  zmath  isi  elib  scopus
    3. Morozov A., “Factorization of differential expansion for antiparallel double-braid knots”, J. High Energy Phys., 2016, no. 9, 135  crossref  mathscinet  zmath  isi  scopus
    4. A. Morozov, Phys. Lett. B, 766 (2017), 291–300  crossref  isi  scopus
    5. A. Mironov, A. Morozov, A. Morozov, P. Ramadevi, V. K. Singh, A. Sleptsov, “Checks of Integrality Properties in Topological Strings”, J. High Energy Phys., 2017, no. 8, 139  crossref  mathscinet  zmath  isi
    6. A. Mironov, A. Morozov, A. Morozov, A. Sleptsov, “Gaussian Distribution of LMOV Numbers”, Nucl. Phys. B, 924 (2017), 1–32  crossref  mathscinet  zmath  isi
    7. Bai C. Jiang J. Liang J. Mironov A. Morozov A. Morozov A. Sleptsov A., “Differential Expansion For Link Polynomials”, Phys. Lett. B, 778 (2018), 197–206  crossref  zmath  isi
    8. Morozov A., “Factorization of Differential Expansion For Non-Rectangular Representations”, Mod. Phys. Lett. A, 33:12 (2018), 1850062  crossref  mathscinet  zmath  isi
    9. Chan Ch.-Ts., Mironov A., Morozov A., Sleptsov A., “Orthogonal Polynomials in Mathematical Physics”, Rev. Math. Phys., 30:6, SI (2018), 1840005  crossref  mathscinet  zmath  isi
    10. Dhara S. Mironov A. Morozov A. Morozov A. Ramadevi P. Singh V.K. Sleptsov A., “Eigenvalue Hypothesis For Multistrand Braids”, Phys. Rev. D, 97:12 (2018), 126015  crossref  isi
    11. Bishler L. Morozov A. Shakirov Sh. Sleptsov A., “On the Block Structure of the Quantum R-Matrix in the Three-Strand Braids”, Int. J. Mod. Phys. A, 33:17 (2018), 1850105  crossref  mathscinet  zmath  isi
    12. Mironov A. Morozov A. Morozov A., “Tangle Blocks in the Theory of Link Invariants”, J. High Energy Phys., 2018, no. 9, 128  crossref  zmath  isi  scopus
    13. Bai C., Jiang J., Liang J., Mironov A., Morozov A., Morozov A., Sleptsov A., “Quantum Racah Matrices Up to Level 3 and Multicolored Link Invariants”, J. Geom. Phys., 132 (2018), 155–180  crossref  mathscinet  zmath  isi  scopus
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