{
  "id": "2103.04471",
  "version": "v1",
  "published": "2021-03-07T22:34:43.000Z",
  "updated": "2021-03-07T22:34:43.000Z",
  "title": "Points of quantum $\\mathrm{SL}_n$ coming from quantum snakes",
  "authors": [
    "Daniel C. Douglas"
  ],
  "comment": "29 pages, 21 figures. arXiv admin note: text overlap with arXiv:2101.06817",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We show that the Fock-Goncharov quantum monodromy matrices satisfy the relations of the quantum special linear group $\\mathrm{SL}_n^q$. The proof employs a quantum version of the technology invented by Fock and Goncharov called snakes. This relationship between higher Teichm\\\"uller theory and quantum group theory is integral to the construction of a $\\mathrm{SL}_n(\\mathbb{C})$-quantum trace map for links in thickened surfaces, developed in a companion paper (arXiv:2101.06817).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-07T22:34:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "32G15",
      "20G42"
    ],
    "keywords": [
      "quantum snakes",
      "fock-goncharov quantum monodromy matrices satisfy",
      "quantum special linear group",
      "quantum trace map",
      "quantum group theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}