On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$

Abstract

Explicit expressions are found for the $6j$ symbols in symmetric representations of quantum ${\mathfrak{su}}_N$ through appropriate hypergeometric Askey-Wilson (q-Racah) polynomials. This generalizes the well-known classical formulas for $U_q({\mathfrak{su}}_2)$ and provides a link to conformal theories and matrix models.

arXiv comment9 pages

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Cited by in corpus (9)

• Tangle blocks in the theory of link invariants
• Multi-Colored Links From 3-strand Braids Carrying Arbitrary Symmetric Representations
• Eigenvalue hypothesis for multi-strand braids
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• HOMFLY for twist knots and exclusive Racah matrices in representation [333]
• Difference of mutant knot invariants and their differential expansion
• Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
• Classical $6j$-symbols for finite dimensional representation of the algebra ${\mathfrak{gl}}_3$
• Entangling gates from cabling of knots