{
  "id": "2411.11546",
  "version": "v1",
  "published": "2024-11-18T13:04:50.000Z",
  "updated": "2024-11-18T13:04:50.000Z",
  "title": "Universal Polynomial $\\mathfrak{so}$ Weight System",
  "authors": [
    "Maxim Kazarian",
    "Zhuoke Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a universal weight system (a function on chord diagrams satisfying the $4$-term relation) taking values in the ring of polynomials in infinitely many variables whose particular specializations are weight systems associated with the Lie algebras $\\mathfrak{so}(N)$, $\\mathfrak{sp}(2M)$, as well as Lie superalgebras $\\mathfrak{osp}(N|2M)$. We extend this weight system to permutations and provide an efficient recursion for its computation. The construction for this weight system extends a similar construction for the universal polynomial weight system responsible for the Lie algebras $\\mathfrak{gl}(N)$ and superalgebras $\\mathfrak{gl}(N|M)$ introduced earlier by the second named author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-18T13:04:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebras",
      "universal polynomial weight system responsible",
      "universal weight system",
      "weight system extends",
      "second named author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}