{
  "annotation_id": "bc461fb3-0a6b-4710-9f8c-f66e4dbd574c",
  "date_created": "2026-03-02T18:01:25.312000Z",
  "date_modified": "2026-03-02T18:01:25.312000Z",
  "file_hash": "3cd32fde4bd0c2be026dcd4884793370d640454c54115f38ae7869384f8c8ee7",
  "private": false,
  "record": {
    "abstract": "The classification of CFTs has an important subproblem, namely classifiying\nthe partition functions for WZW theories. This subproblem is intimately\nconnected to the modular behaviour of the characters of affine algebras. This\npaper addresses the classification of the largest class of these -- the natural\ngeneralization to any affine algebra of the A-series, D-series, and\n$E_7$-exceptional appearing in the A-D-E classification of\nCappelli-Itzykson-Zuber for $A_1^{(1)}$. We give a programme for classifying\nthese for any algebra, and explicitly do this for the most interesting case:\n$A_r^{(1)}$ at any level k. The exceptionals appear at (r,k)=(1,16), (2,9),\n(3,8), (4,5), (7,4), (8,3) and (15,2).",
    "arxiv_id": "q-alg/9510026",
    "authors": [
      "Terry Gannon"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "title": "Kac-Peterson, Perron-Frobenius, and the Classification of Conformal   Field Theories",
    "url": "https://arxiv.org/abs/q-alg/9510026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f0defbc1-4a32-47ac-b01a-5b289f8ee3b4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}