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

It is well known that the SU(2)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)SU(2) Chern–Simons field theory. Using isotopy equivalence of SU(N)SU(N) Chern–Simons functional integrals over three-balls with one or more S2S2 boundaries with punctures, we obtain identities to be satisfied by the SU(N)SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N)SU(N) representations. Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links. These results are useful for verifying conjectures in topological string theory.