{
  "annotation_id": "e2d744e9-7d54-4ea7-84b1-f10e9269a598",
  "date_created": "2026-03-02T18:01:24.967000Z",
  "date_modified": "2026-03-02T18:01:24.967000Z",
  "file_hash": "ee90d7df92f4c6d2d436537463c4f36cfed40055e6f70ddad5411438cf97c16b",
  "private": false,
  "record": {
    "abstract": "The admissible modules for $\\hat{sl}_2$ are studied from the point of view of\nvertex operator algebra. If $l$ is rational such that $l+2={p\\over q}$ for some\ncoprime positive integers $p\\ge 2$ and $q$, Kac and Wakimoto found finitely\nmany distinguished irreducible representations for $\\hat{sl}_2$, called\nadmissible representations. In this paper we prove that the vertex operator\nalgebra $L(l,0)$ associated to irreducible highest weight representation of $l$\nis not rational if $l$ is not a positive integer. However if we change the\nVirasoro algebra in certain way, $L(l,0)$ becomes a rational vertex operator\nalgebra whose irreducible representations are exactly those admissible\nrepresentations. We show that the $q$-dimensions with respect to the new\nVirasoro algebra are modular functions. We aslo calculate the fusions rules.",
    "arxiv_id": "q-alg/9509026",
    "authors": [
      "Chongying Dong",
      "Haisheng Li",
      "Geoffrey Mason"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Vertex operator algebras associated to admissible representations of   $\\hat{sl}_2$",
    "url": "https://arxiv.org/abs/q-alg/9509026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e88afd46-cce5-46ba-bd66-e58be4eaddeb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}