{
  "annotation_id": "97108c9a-77ad-414c-88c7-a6db218dabe5",
  "date_created": "2026-03-02T18:02:51.561000Z",
  "date_modified": "2026-03-02T18:02:51.561000Z",
  "file_hash": "5b7d349b0ed3b87554157ee5e8af5c2bccd3a6d344bc13d06f3f9f5094544ea9",
  "private": false,
  "record": {
    "abstract": "Consider the evolution $$ \\frac{\\pl m_\\iy}{\\pl t_n}=\\Lb^n m_\\iy, \\frac{\\pl\nm_\\iy}{\\pl s_n}=-m_\\iy(\\Lb^\\top)^n, $$ on bi- or semi-infinite matrices\n$m_\\iy=m_\\iy(t,s)$, with skew-symmetric initial data $m_{\\iy}(0,0)$. Then,\n$m_\\iy(t,-t)$ is skew-symmetric, and so the determinants of the successive\n\"upper-left corners\" vanish or are squares of Pfaffians. In this paper, we\ninvestigate the rich nature of these Pfaffians, as functions of t. This problem\nis motivated by questions concerning the spectrum of symmetric and symplectic\nrandom matrix ensembles.",
    "arxiv_id": "solv-int/9909010",
    "authors": [
      "M. Adler",
      "T. Shiota",
      "P. van Moerbeke"
    ],
    "categories": [
      "solv-int",
      "adap-org",
      "hep-th",
      "nlin.AO",
      "nlin.SI"
    ],
    "title": "Pfaff tau-functions",
    "url": "https://arxiv.org/abs/solv-int/9909010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "969278bd-4dce-4f2f-8c05-a6afa4d1c7ab",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}