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

TL;DR

This paper derives explicit formulas for $6j$-symbols in symmetric representations of quantum $ ext{su}_N$, extending classical results for $ ext{su}_2$ and connecting to conformal theories and matrix models.

Contribution

It provides a generalization of $6j$-symbol formulas for symmetric representations of quantum $ ext{su}_N$ using hypergeometric polynomials.

Findings

Explicit $6j$-symbol expressions for symmetric $U_q( ext{su}_N)$ representations

Extension of classical $U_q( ext{su}_2)$ formulas to higher $N$

Links to conformal theories and matrix models

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.