Tensor Diagrams And Chebyshev Polynomials

In this paper, we describe a class of elements in the ring of SL(V)-invariant polynomial functions on the space of configurations of vectors and linear forms of a 3D vector space V. These elements are related to one another by an induction formula using Chebyshev polynomials. We also investigate the relation between these polynomials and G. Lusztig's dual canonical basis in tensor products of representations of Uq(sl(3)(C)).