{
  "annotation_id": "bdbc9243-5709-46a0-b3c5-384c35f37199",
  "date_created": "2026-03-02T18:01:21.881000Z",
  "date_modified": "2026-03-02T18:01:21.881000Z",
  "file_hash": "9af29661247795088b04b960d23ec62428386eff57358913de796bd5debad189",
  "private": false,
  "record": {
    "abstract": "Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\\times\nS_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients\n(IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\\times\nS_{f_{2}}\\uparrow D_{f}(n)$ with $f\\leq 4$ up to a normalization factor are\nderived by using the linear equation method. Weyl tableaus for the\ncorresponding Gel\u0027fand basis of SO(n) are defined. The assimilation method for\nobtaining CG coefficients of SO(n) in the Gel\u0027fand basis for no modification\nrule involved couplings from IDCs of Brauer algebra are proposed. Some\nisoscalar factors of $SO(n)\\supset SO(n-1)$ for the resulting irrep\n$[\\lambda_{1},~\\lambda_{2},~ \\lambda_{3},~\\lambda_{4},\\dot{0}]$ with\n$\\sum\\limits_{i=1}^{4}\\lambda_{i}\\leq .",
    "arxiv_id": "physics/9803045",
    "authors": [
      "Feng Pan",
      "Shi-hai Dong",
      "J. P. Draayer"
    ],
    "categories": [
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1088/0305-4470/31/40/016",
    "journal_ref": "J.Phys.A31:8247-8266,1998",
    "title": "The induced representations of Brauer algebra and the Clebsch-Gordan   coefficients of SO(n)",
    "url": "https://arxiv.org/abs/physics/9803045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a73b9949-202e-4a2c-8f08-6e6375073880",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}