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This article is cited in 29 scientific papers (total in 29 papers)
METHODS OF THEORETICAL PHYSICS
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.
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
Linking options:
https://www.mathnet.ru/eng/jetpl5007 https://www.mathnet.ru/eng/jetpl/v104/i1/p52
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Abstract page: | 383 | Full-text PDF : | 143 | References: | 59 | First page: | 19 |
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