{
  "annotation_id": "31f81512-e6f5-4142-86e3-ee8071c7749c",
  "date_created": "2026-03-02T18:01:28.406000Z",
  "date_modified": "2026-03-02T18:01:28.406000Z",
  "file_hash": "d482f361fbca1f991d05ac2cb23f9c99644b7b3f74ef1a2ea3db028ad705e82e",
  "private": false,
  "record": {
    "abstract": "We introduce an elliptic algebra $U_{q,p}(\\hat{sl_2})$ with $p=q^{2r} (r\\in\n\\R_{\u003e0})$ and present its free boson representation at generic level $k$. We\nshow that this algebra governs a structure of the space of states in the\n$k-$fusion RSOS model specified by a pair of positive integers $(r,k)$, or\nequivalently a $q-$deformation of the coset conformal field theory\n$SU(2)_k\\times SU(2)_{r-k-2}/SU(2)_{r-2}$. Extending the work by Lukyanov and\nPugai corresponding to the case $k=1$, we gives a full set of screening\noperators for $k\u003e1$. The algebra $U_{q,p}(\\hat{sl_2})$ has two interesting\ndegeneration limits, $p\\to 0$ and $p\\to 1$. The former limit yields the quantum\naffine algebra $U_{q}(\\hat{sl_2})$ whereas the latter yields the algebra ${\\cal\nA}_{\\hbar,\\eta}(\\hat{sl_2})$, the scaling limit of the elliptic algebra ${\\cal\nA}_{q,p}(\\hat{sl_2})$. Using this correspondence, we also obtain the highest\ncomponent of two types of vertex operators which can be regarded as\n$q-$deformations of the primary fields in the coset conformal field theory.",
    "arxiv_id": "q-alg/9709013",
    "authors": [
      "Hitoshi Konno"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1007/s002200050394",
    "title": "An Elliptic Algebra $U_{q,p}(\\hat{sl_2})$ and the Fusion RSOS Model",
    "url": "https://arxiv.org/abs/q-alg/9709013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "37cf6fba-1748-4eef-b6de-7ca6e1f55a89",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}