I have some rather specific questions about the MOY knot invariant which have come up as Sabin Cautis and I have been thinking about Khovanov-Rozansky homology. I’ll start by explaining the following “theorem” and then I’ll ask some questions about it. Hopefully someone (for eg. Scott) will be able to answer them.

Consider closed crossingless Reshetikhin-Turaev diagrams for sl(n) where all strands are labelled by 1 or 2. This means that we look at oriented planar graphs with all edges either labelled 1 or 2, and each vertex trivalent with either two single edges and one double edge and matching orientations.

We can think of such a graph as being related to the representation theory of (quantum) sl(n). The single strands correspond to the standard representation and the double strands to The vertices correspond to morphisms of representations (for example ). Within this representation theory context, each graph G can be evaluated to a Laurent polynomial c(G) (an element of the trivial representation of quantum sl(n)).