{
  "annotation_id": "71739912-cbff-40bc-b056-d4d836fa99a5",
  "date_created": "2026-03-02T18:01:25.355000Z",
  "date_modified": "2026-03-02T18:01:25.355000Z",
  "file_hash": "6582769f470ab449bb0be4692789774b5d2a26de8441ccf58246b5ea4e83eebe",
  "private": false,
  "record": {
    "abstract": "This paper is a sequel to \"Localization of $\\frak{u}$-modules. I\",\nhep-th/9411050. We are starting here the geometric study of the tensor category\n$\\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of\nfinite type) at a root of unity. The main results establish isomorphisms\nbetween homogeneous components of irreducible objects in $\\cal{C}$ and spaces\nof vanishing cycles at the origin of certain Goresky-MacPherson sheaves on\nconfiguration spaces; establish isomorphisms of the stalks at the origin of the\nabove GM sheaves with certain Hochschild complexes (which compute the\nHochschild homology of a certain \"triangular\" subalgebra of our quantum group\nwith coefficients in the coresponding irreducible representation); establish\nthe analogous results for tensor products of irreducibles. In geometry, the\ntensor product of representations corresponds to a \"fusion\" of sheaves on\nconfiguration spaces --- operation defined using the functor of nearby cycles.",
    "arxiv_id": "q-alg/9412017",
    "authors": [
      "M. Finkelberg",
      "V. Schechtman"
    ],
    "categories": [
      "q-alg",
      "alg-geom",
      "math.AG",
      "math.QA"
    ],
    "title": "Localization of $\\frak{u}$-modules. II. Configuration spaces and quantum   groups",
    "url": "https://arxiv.org/abs/q-alg/9412017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9f93db3-ddab-4e88-8404-a9f90dcb2b1c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}