{
  "id": "1609.03501",
  "version": "v1",
  "published": "2016-09-12T17:48:14.000Z",
  "updated": "2016-09-12T17:48:14.000Z",
  "title": "Tensor diagrams and Chebyshev polynomials",
  "authors": [
    "Lisa Lamberti"
  ],
  "comment": "37 pages. Comments are welcome",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "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 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 $U_q(\\mathrm{sl}_3(\\mathbb C)).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-12T17:48:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chebyshev polynomials",
      "tensor diagrams",
      "lusztigs dual canonical basis",
      "invariant polynomial functions",
      "tensor products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}