{
  "annotation_id": "e50b4ddd-4bfd-4cea-8bba-2c1e8b4b0f18",
  "date_created": "2026-03-02T18:01:28.068000Z",
  "date_modified": "2026-03-02T18:01:28.068000Z",
  "file_hash": "7aab19a8761876795ee276904c4e77a75bbf7ee0a6e251baddfc1234742b7451",
  "private": false,
  "record": {
    "abstract": "We compare two natural bases for the invariant space of a tensor product of\nirreducible representations of A_2, or sl(3). One basis is the web basis,\ndefined from a skein theory called the combinatorial A_2 spider. The other\nbasis is the dual canonical basis, the dual of the basis defined by Lusztig and\nKashiwara. For sl(2) or A_1, the web bases have been discovered many times and\nwere recently shown to be dual canonical by Frenkel and Khovanov.\n  We prove that for sl(3), the two bases eventually diverge even though they\nagree in many small cases. The first disagreement comes in the invariant space\nInv((V^+ tensor V^+ tensor V^- tensor V^-)^{tensor 3}), where V^+ and V^- are\nthe two 3-dimensional representations of sl(3). If the tensor factors are\nlisted in the indicated order, only 511 of the 512 invariant basis vectors\ncoincide.",
    "arxiv_id": "q-alg/9712046",
    "authors": [
      "Mikhail Khovanov",
      "Greg Kuperberg"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "Pacific J. Math. 188 (1999), 129--153",
    "title": "Web bases for sl(3) are not dual canonical",
    "url": "https://arxiv.org/abs/q-alg/9712046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "63a7fdf5-6257-4fac-a68c-a0155e512fd8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}