{
  "annotation_id": "a984f129-ef5c-4681-b6af-658c2e35d199",
  "date_created": "2026-03-02T18:01:28.411000Z",
  "date_modified": "2026-03-02T18:01:28.411000Z",
  "file_hash": "0b56813f56e964b33221c667d61676178cbd5b51f096053f08dfbe69ed6ec62f",
  "private": false,
  "record": {
    "abstract": "We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal\nfield theories, affine Kac-Moody algebras at positive integer level, and\nquantum groups at roots of unity. Using properties of the modular matrix $S$,\nwe find small sets of primary fields (equivalently, sets of highest weights)\nwhich can be identified with the variables of a polynomial realization of the\n$A_r$ fusion algebra at level $k$. We prove that for many choices of rank $r$\nand level $k$, the number of these variables is the minimum possible, and we\nconjecture that it is in fact minimal for most $r$ and $k$. We also find new,\nsystematic sources of zeros in the modular matrix $S$. In addition, we obtain a\nformula relating the entries of $S$ at fixed points, to entries of $S$ at\nsmaller ranks and levels. Finally, we identify the number fields generated over\nthe rationals by the entries of $S$, and by the fusion (Verlinde) eigenvalues.",
    "arxiv_id": "q-alg/9709039",
    "authors": [
      "T. Gannon",
      "M. A. Walton"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1007/s002200050695",
    "journal_ref": "Commun.Math.Phys.206:1-22,1999",
    "title": "On Fusion Algebras and Modular Matrices",
    "url": "https://arxiv.org/abs/q-alg/9709039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4728bd6d-c152-4caf-805d-e04cb6c23ec4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}