  We compute the invariants for a class of knots and links in arbitrary
representations in $S^3/\mathbb{Z}_p$ in the large $k$ (level), large $N$
(rank) limit, keeping $N/(k+N)=\lambda$ fixed, in $U(N)$ and $Sp(N)$
Chern-Simons theories. Using the relation between the saddle point description
and collective field theory, we first find that the invariants for the Hopf
link and unknot are given by the on shell collective field theory action. We
next show that the results of these two invariants can be used to compute the
invariants of other torus knots and links. We also discuss the large $N$ phase
structure of the Hopf link invariant and observe that the same may admit a
Douglas-Kazakov type phase transition depending on the choice of
representations and $\lambda$.
