  Knot and link polynomials are topological invariants calculated from the
expectation value of loop operators in topological field theories. In 3D
Chern-Simons theory, these invariants can be found from crossing and braiding
matrices of four-point conformal blocks of the boundary 2D CFT. We calculate
crossing and braiding matrices for $W_N$ conformal blocks with one component in
the fundamental representation and another in a rectangular representation of
$SU(N)$, which can be used to obtain HOMFLY knot and link invariants for these
cases. We also discuss how our approach can be generalized to invariants in
higher-representations of $W_N$ algebra.
