{
  "annotation_id": "019b6d7e-98fb-4732-9988-45f5da237456",
  "date_created": "2026-03-02T18:02:51.572000Z",
  "date_modified": "2026-03-02T18:02:51.572000Z",
  "file_hash": "5d3227639a2ef91b0fb92ad3f21269746c2db1242c825b7e459af2c2b27dc82f",
  "private": false,
  "record": {
    "abstract": "We study the Pfaff lattice, introduced by us in the context of a Lie algebra\nsplitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We\nestablish a set of bilinear identities, which we show to be equivalent to the\nPfaff Lattice. In the semi-infinite case, the tau-functions are Pfaffians;\ninteresting examples are the matrix integrals over symmetric matrices\n(symmetric matrix integrals) and matrix integrals over self-dual quaternionic\nHermitean matrices (symplectic matrix integrals).\n  There is a striking parallel of the Pfaff lattice with the Toda lattice, and\nmore so, there is a map from one to the other. In particular, we exhibit two\nmaps, dual to each other,\n  (i) from the the Hermitean matrix integrals to the symmetric matrix\nintegrals, and\n  (ii) from the Hermitean matrix integrals to the symplectic matrix integrals.\n  The map is given by the skew-Borel decomposition of a skew-symmetric\noperator. We give explicit examples for the classical weights.",
    "arxiv_id": "solv-int/9912008",
    "authors": [
      "M. Adler",
      "P. van Moerbeke"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "The Pfaff lattice, Matrix integrals and a map from Toda to Pfaff",
    "url": "https://arxiv.org/abs/solv-int/9912008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "411e5114-3c6f-429d-b059-1517111bfe70",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}