Tensor diagrams and Chebyshev polynomials

Lisa Lamberti

Published 2016-09-12Version 1

In this paper, we describe a class of elements in the ring of $\mathrm{SL}(V)$-invariant polynomial functions on the space of configurations of vectors and linear forms of a 3-dimensional vector space $V.$ These elements are determined by Chebyshev polynomials of the first and second kind with coefficients. We also investigate the relation between these polynomials and Lusztig's dual canonical basis in tensor products of representations of $U_q(\mathrm{sl}_3(\mathbb C)).$