This question is a spin-off from [Sammy Black's question on super Temperley-Lieb](https://mathoverflow.net/questions/3299/). Please see there for the background. The short version is that Sammy defines the Temperley-Lieb at index d as the algebra of sl(2) intertwiners of d copies of the defining rep of sl(2) (and then asks about a supersymmetric version).


My question: in what ways does Sammy's story extend to other simple Lie groups, e.g. sl(3)? For example, I think that the Schur-Weyl duality still holds, so that HomUsl(3)(V⊗d) is a quotient of the group algebra of the symmetric group Sd (here V is the defining representation of sl(3)). Is it something like the Young Tableaux with three rows? And is there a diagrammatic description of this algebra?



Is there a version of Temperley-Lieb using sl(3) rather than sl(2)?
Cvitanovic is great for the groups themselves. But if you care about the quantum group (and this is really where TL shines) some good references are [Kuperberg's work on Spiders](http://arxiv.org/abs/q-alg/9712003) and [Scott Morrison's thesis](http://arxiv.org/abs/0704.1503).


