{
  "annotation_id": "ab26d17a-2396-4212-af88-4708957f03dc",
  "date_created": "2026-03-02T18:01:28.069000Z",
  "date_modified": "2026-03-02T18:01:28.069000Z",
  "file_hash": "08015a2640d12f164d39105941896da8fd3ff26f204f7af1aede5ee77d40a16b",
  "private": false,
  "record": {
    "abstract": "We discuss some aspects of the representation theory of the deformed Virasoro\nalgebra $\\virpq$. In particular, we give a proof of the formula for the Kac\ndeterminant and then determine the center of $\\virpq$ for $q$ a primitive N-th\nroot of unity. We derive explicit expressions for the generators of the center\nin the limit $t=qp^{-1}\\to \\infty$ and elucidate the connection to the\nHall-Littlewood symmetric functions. Furthermore, we argue that for\n$q=\\sqrtN{1}$ the algebra describes `Gentile statistics\u0027 of order $N-1$, i.e.,\na situation in which at most $N-1$ particles can occupy the same state.",
    "arxiv_id": "q-alg/9710026",
    "authors": [
      "P. Bouwknegt",
      "K. Pilch"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1007/s002200050421",
    "journal_ref": "Commun. Math. Phys. 196 (1998) 249-288",
    "title": "The deformed Virasoro algebra at roots of unity",
    "url": "https://arxiv.org/abs/q-alg/9710026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b37f38f1-7f04-46ce-92c3-8e2f7f0aa699",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}