{
  "annotation_id": "41420e42-d96f-480e-92a2-b5ea197032c1",
  "date_created": "2026-03-02T18:02:40.775000Z",
  "date_modified": "2026-03-02T18:02:40.775000Z",
  "file_hash": "3e2d8267be9c804580a0cf8e4891937c94d2706a3981e9834a81352971a82cbf",
  "private": false,
  "record": {
    "abstract": "A complementary group to SU(n) is found that realizes all features of the\nLittlewood rule for Kronecker products of SU(n) representations. This is\naccomplished by considering a state of SU(n) to be a special Gel\u0027fand state of\nthe complementary group {\\cal U}(2n-2). The labels of {\\cal U}(2n-2) can be\nused as the outer multiplicity labels needed to distinguish multiple\noccurrences of irreducible representations (irreps) in the SU(n)\\times\nSU(n)\\downarrow SU(n) decomposition that is obtained from the Littlewood rule.\nFurthermore, this realization can be used to determine SU(n)\\supset\nSU(n-1)\\times U(1) Reduced Wigner Coefficients (RWCs) and Clebsch-Gordan\nCoefficients (CGCs) of SU(n), using algebraic or numeric methods, in either the\ncanonical or a noncanonical basis. The method is recursive in that it uses\nsimpler RWCs or CGCs with one symmetric irrep in conjunction with standard\nrecoupling procedures. New explicit formulae for the multiplicity for SU(3) and\nSU(4) are used to illustrate the theory.",
    "arxiv_id": "quant-ph/9704014",
    "authors": [
      "Feng Pan",
      "J. P. Draayer"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532555",
    "journal_ref": "J.Math.Phys. 39 (1998) 5631-5641",
    "title": "A complementary group technique for a resolution of the outer   multiplicity problem of SU(n): (I) Littlewood rule and a complementary group   of SU(n)",
    "url": "https://arxiv.org/abs/quant-ph/9704014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "795d03c7-6941-449d-9ab1-d9bf80be2cdf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}