{
  "annotation_id": "1a58bcc5-1721-46a8-868a-df8ef9149280",
  "date_created": "2026-03-02T18:01:27.794000Z",
  "date_modified": "2026-03-02T18:01:27.794000Z",
  "file_hash": "71bb6d3b2f67b0cabd53e0b5faf012e9c90f98b4ae194e73678c536e253c4f18",
  "private": false,
  "record": {
    "abstract": "We use an explicit isomorphism from the representation ring of the quantum\ngroup U_q(sl(N)) to the Homfly skein of the annulus, to determine an element of\nthe skein which is the image of the mth Adams operator, \\psi_m, on the\nfundamental representation, c_1. This element is a linear combination of m very\nsimple m-string braids. Using this skein element, we show that the Vassiliev\ninvariant of degree n in the power series expansion of the U_q(sl(N)) quantum\ninvariant of a knot coloured by \\psi_m(c_1) is the canonical Vassiliev\ninvariant with weight system W_n\\psi_m^{(n)} where W_n is the weight system for\nthe Vassiliev invariant of degree n in the expansion of the quantum invariant\nof the knot coloured by c_1 and \\psi_m^{(n)} is the Adams operator on n-chord\ndiagrams defined by Bar-Natan.",
    "arxiv_id": "q-alg/9711015",
    "authors": [
      "A. K. Aiston"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Adams operators and knot decorations",
    "url": "https://arxiv.org/abs/q-alg/9711015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cfb13529-38c0-4f5e-93f4-bc2e257e1be9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}