English

Tensor diagrams and Chebyshev polynomials

Combinatorics 2018-10-19 v3 Representation Theory

Abstract

In this paper, we describe a class of elements in the ring of SL(V)\mathrm{SL}(V)-invariant polynomial functions on the space of configurations of vectors and linear forms of a 3-dimensional vector space V.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(sl3(C)).U_q(\mathfrak{sl}_3(\mathbb C)).

Keywords

Cite

@article{arxiv.1609.03501,
  title  = {Tensor diagrams and Chebyshev polynomials},
  author = {Lisa Lamberti},
  journal= {arXiv preprint arXiv:1609.03501},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T15:47:25.037Z