Tensor diagrams and Chebyshev polynomials

Abstract

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 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 $U_q({\mathfrak{sl}}_3(\mathbb{C})).$

41 pages. Exposition shortened and clarified following the suggestions of the anonymous referees. Figures added. Comments are welcome

References in corpus (3)

• A positive basis for surface skein algebras
• Greedy bases in rank 2 quantum cluster algebras
• A characterisation of indecomposable web-modules over Khovanov-Kuperberg Algebras

Cited by in corpus (1)

• Symbol Alphabets from Tensor Diagrams