  We characterise the cabling operations on the weight systems of finite type
knot invariants. The eigenvectors and eigenvalues of this family of operations
are described over the cable eigenbasis. The action of immanent weight systems
on general Feynman diagrams is considered, and the highest eigenvalue cabling
eigenvectors are shown to be dual to the immanent weight systems. Using these
results, we prove a recent conjecture of Bar-Natan and Garoufalidis on cablings
of weight systems.
