{
  "annotation_id": "861769df-9281-4c71-b6fe-6a51bc6f0747",
  "date_created": "2026-03-02T18:01:28.528000Z",
  "date_modified": "2026-03-02T18:01:28.528000Z",
  "file_hash": "da7787a8ad6bb566454c6f2aa693e1f18c41813b9e59536f745ef1aad9ca617d",
  "private": false,
  "record": {
    "abstract": "Representation theory for the Jordanian quantum algebra $U=U_h(sl(2))$ is\ndeveloped. Closed form expressions are given for the action of the generators\nof U on the basis vectors of finite dimensional irreducible representations. It\nis shown how representation theory of U has a close connection to combinatorial\nidentities involving summation formulas. A general formula is obtained for the\nClebsch-Gordan coefficients $C^{j_1,j_2,j}_{n_1,n_2,m}(h)$ of U. These\nClebsch-Gordan coefficients are shown to coincide with those of su(2) for\n$n_1+n_2 \\leq m$, but for $n_1+n_2 \u003e m$ they are in general a nonzero monomial\nin $h^{n_1+n_2-m}$.",
    "arxiv_id": "q-alg/9703011",
    "authors": [
      "Joris Van der Jeugt"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/31/5/017",
    "title": "Representations and Clebsch-Gordan coefficients for the Jordanian   quantum algebra U_h(sl(2))",
    "url": "https://arxiv.org/abs/q-alg/9703011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7591058e-0c1b-42ad-b659-4f21e7480dfb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}