{
  "annotation_id": "7b8cee45-5fbe-4f32-aa1d-d2dec7a34135",
  "date_created": "2026-03-02T18:01:28.694000Z",
  "date_modified": "2026-03-02T18:01:28.694000Z",
  "file_hash": "d5c8774fa4b9ea3a9b2a9c00da324ed065501f870ca4c5a6d8b83dc586768d64",
  "private": false,
  "record": {
    "abstract": "Recently Varagnolo and Vasserot established that the q-deformed Fock spaces\ndue to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum\ntoroidal algebra $U_q(sl_n,tor)$ (n \u003e 2) with the level (0,1). In the present\narticle we propose a more detailed proof of this fact then the one given by\nVaragnolo and Vasserot. The proof is based on certain non-trivial properties of\nCherednik\u0027s commuting difference operators. The quantum toroidal action on the\nFock space depends on a certain parameter. We find that with a specific choice\nof this parameter the action on the Fock spaces gives rise to the toroidal\naction on irreducible level-1 highest weight modules of the affine quantum\nalgebra $U_q(\\hat{sl}_n)$. Similarly, by a specific choice of the parameter,\nthe level (1,0) vertex representation of the quantum toroidal algebra gives\nrise to a $U_q(sl_n,tor)$-module structure on irreducible level-1 highest\nweight $U_q(\\hat{sl}_n)$-modules.",
    "arxiv_id": "q-alg/9702024",
    "authors": [
      "Y. Saito",
      "K. Takemura",
      "D. Uglov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Toroidal actions on level 1 modules of U_q(\\hat{sl_n})",
    "url": "https://arxiv.org/abs/q-alg/9702024"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cb0a88f7-e942-4bf2-a945-5945795c2d6b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}