{
  "annotation_id": "7c9040c6-bf98-44cd-9d3f-3628e5ab7d71",
  "date_created": "2026-03-02T18:01:27.797000Z",
  "date_modified": "2026-03-02T18:01:27.797000Z",
  "file_hash": "68ee105e6d8ce9fdc7efbcde57e28d9530662e004bd6fcc87a0699f6ae81e4d3",
  "private": false,
  "record": {
    "abstract": "For any module $M$ over small quantum group one defines the support variety\nusing construction from the theory of restricted Lie algebras. It is a closed\nconical subset of nilpotent cone of the corresponding Lie algebra. If module\n$M$ is a module over the quantum group $U_{\\xi}$ with divided powers then its\nsupport variety is invariant under the action of the corresponding algebraic\ngroup. In this case we relate codimension $2a$ of the support variety of $M$ in\nnilpotent cone and dimension of $M$. Namely, we prove that $\\dim M$ is `almost\u0027\ndivisible by $l^a$. Further, we give an a priori estimate for support variety\nof a module in a given linkage class. We compute the support varieties for Weyl\nmodules. Also we compute the support varieties for tilting modules over quantum\n$SL_n$ and verify in this case Humphreys\u0027 Conjecture which relates support\nvarieties of tilting modules with Lusztig\u0027s bijection between nilpotent orbits\nand two-sided cells in the affine Weyl group.",
    "arxiv_id": "q-alg/9711008",
    "authors": [
      "V. Ostrik"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Support varieties for quantum groups",
    "url": "https://arxiv.org/abs/q-alg/9711008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41760cf6-0ad4-4ef2-8bcf-bc5b9e0cc7b0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}