{
  "annotation_id": "2a2e8b5b-d39f-41a1-9cd4-792d9f3b6330",
  "date_created": "2026-03-02T18:01:27.798000Z",
  "date_modified": "2026-03-02T18:01:27.798000Z",
  "file_hash": "ee63e0de4ce3318407f13339f4b08f95fd1c6e0201b35d4bc29dda5bddf526c5",
  "private": false,
  "record": {
    "abstract": "The spectral decomposition of the path space of the vertex model associated\nto the level $l$ representation of the quantized affine algebra\n$U_q(\\hat{sl}_n)$ is studied. The spectrum and its degeneracy are parametrized\nby skew Young diagrams and what we call nonmovable tableaux on them,\nrespectively. As a result we obtain the characters for the degeneracy of the\nspectrum in terms of an alternating sum of skew Schur functions. Also studied\nare new combinatorial descriptions (spectral decomposition) of the Kostka\nnumbers and the Kostka--Foulkes polynomials. As an application we give a new\nproof of Nakayashiki--Yamada\u0027s theorem about the branching functions of the\nlevel $l$ basic representation $l\\Lambda_k$ of $\\hat{sl}_n$ and a\ngeneralization of the theorem.",
    "arxiv_id": "q-alg/9711009",
    "authors": [
      "Anatol N. Kirillov",
      "Atsuo Kuniba",
      "Tomoki Nakanishi"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1016/S0550-3213(98)00351-4",
    "journal_ref": "Nucl. Phys. B529 [PM] (1998) 611-638",
    "title": "Skew Young diagram method in spectral decomposition of integrable   lattice models II: Higher levels",
    "url": "https://arxiv.org/abs/q-alg/9711009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "39cbfc2d-9239-41e8-bf8e-239b80e7549a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}