{
  "annotation_id": "72af83d7-8a11-488a-a980-90b221edb588",
  "date_created": "2026-03-02T18:01:24.719000Z",
  "date_modified": "2026-03-02T18:01:24.719000Z",
  "file_hash": "99cb92d54565eb8e2c971d54e75f59a6f01a6b2833aff2c78bd5ea1caa1579dd",
  "private": false,
  "record": {
    "abstract": "This note is an attempt to extend \"Geometric Langlands Conjecture\" from\nalgebraic curves to algebraic surfaces. We introduce certain Hecke-type\noperators on vector bundles on an algebraic surface. The crucial observation is\nthat the algebra generated by the Hecke operators turns out to be a homomorphic\nimage of the {\\it quantum toroidal algebra}. The latter is a quantization, in\nthe spirit of Drinfeld-Jimbo, of the universal enveloping algebra of the\nuniversal central extension of a \"double-loop\" Lie algebra. This yields, in\nparticular, a new geometric construction of affine quantum groups of types A, D\nE in terms of Hecke operators for an elliptic surface.",
    "arxiv_id": "q-alg/9502013",
    "authors": [
      "Victor Ginzburg",
      "Mikhail Kapranov",
      "Eric Vasserot"
    ],
    "categories": [
      "q-alg",
      "alg-geom",
      "math.AG",
      "math.QA"
    ],
    "title": "Langlands Reciprocity for Algebraic Surfaces",
    "url": "https://arxiv.org/abs/q-alg/9502013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e8706e07-cdec-4edd-b9d5-21033fd64746",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}