SU(N) quantum Racah coefficients & non-torus links

Understand

It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory.

• Using isotopy equivalence of SU(N) Chern-Simons functional integrals over three balls with one or more $S^2$ boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients.
• This enables evaluation of the coefficients for a class of SU(N) representations.
• Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links.