{
  "annotation_id": "de666897-8ec3-48a6-9a36-98d84ad0e6e5",
  "date_created": "2026-03-02T18:01:28.348000Z",
  "date_modified": "2026-03-02T18:01:28.348000Z",
  "file_hash": "0ac990bd928e80f688bdc9c717173d369842d0e2151a2ffb730328555a91d039",
  "private": false,
  "record": {
    "abstract": "We review and motivate recently-observed relationships between exactly\nsolvable lattice models and modular representations of Hecke algebras. Firstly,\nwe describe how the set of $n$-regular partitions label both of the following\nclasses of objects:\n  1. The spectrum of unrestricted solid-on-solid lattice models based on\nlevel-1 representations of the affine algebras $\\sl_n$,\n  2. The irreducible representations of type-A Hecke algebras at roots of\nunity: $H_m(\\sqrt[n]{1})$.\n  Secondly, we show that a certain subset of the $n$-regular partitions label\nboth of the following classes of objects:\n  1. The spectrum of restricted solid-on-solid lattice models based on cosets\nof affine algebras $(sl(n)^_1 \\times sl(n)^_1)/ sl(n)^_2$.\n  2. Jantzen-Seitz (JS) representations of $H_m(\\sqrt[n]{1})$: irreducible\nrepresentations that remain irreducible under restriction to\n$H_{m-1}(\\sqrt[n]{1})$.\n  Using the above relationships, we characterise the JS representations of\n$H_m(\\sqrt[n]{1})$ and show that the generating series that count them are\nbranching functions of affine $\\sl_n$.",
    "arxiv_id": "q-alg/9701021",
    "authors": [
      "Omar Foda",
      "Bernard Leclerc",
      "Masato Okado",
      "Jean-Yves Thibon",
      "Trevor A. Welsh"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "title": "Combinatorics of solvable lattice models, and modular representations of   Hecke algebras",
    "url": "https://arxiv.org/abs/q-alg/9701021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "047798a2-bb8b-42d4-ba7e-6af1af117cbe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}