New symmetries for the $U_q(s{l}_N)$ 6-j symbols from the Eigenvalue conjecture

Abstract

In the present paper we discuss the eigenvalue conjecture, suggested in 2012, in the particular case of $U_q(s{l}_2)$. The eigenvalue conjecture provides a certain symmetry for Racah coefficients and we prove that \textbf{the eigenvalue conjecture is provided by the Regge symmetry} for $U_q(s{l}_2)$, when three representations coincide. This in perspective provides us a kind of generalization of the Regge symmetry to arbitrary $U_q(s{l}_N)$.

arXiv comment9 pages

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Cited by in corpus (11)

• Multi-Colored Links From 3-strand Braids Carrying Arbitrary Symmetric Representations
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Quantum $\mathcal{R}$-matrices as universal qubit gates
• A new symmetry of the colored Alexander polynomial
• Pentad and triangular structures behind the Racah matrices
• Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
• Interplay between symmetries of quantum 6-j symbols and the eigenvalue hypothesis
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Vogel's universality and the classification problem for Jacobi identities
• Tug-the-hook symmetry for quantum 6j-symbols
• Multistrand Eigenvalue conjecture and Racah symmetries