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 $U_q(s{l}_N)$.

9 pages

References in corpus (3)

• Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations
• Colored knot polynomials for Pretzel knots and links of arbitrary genus
• A note on colored HOMFLY polynomials for hyperbolic knots from WZW models

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• Vogel's universality and the classification problem for Jacobi identities
• Tug-the-hook symmetry for quantum 6j-symbols
• Multistrand Eigenvalue conjecture and Racah symmetries