{
  "annotation_id": "889fbd40-f584-445f-9d27-fe7b7e72562f",
  "date_created": "2026-03-02T18:02:51.219000Z",
  "date_modified": "2026-03-02T18:02:51.219000Z",
  "file_hash": "e0817e2f4d66a74a1c400374bbd6b11a85da07656f19328622f92ebebc8a8cf8",
  "private": false,
  "record": {
    "abstract": "We construct the vertex operator representation for the Affine Kac-Moody\n$SL(M+K+1)$ algebra, which is relevant for the construction of the soliton\nsolutions of the constrained KP hierarchies. The oscillators involved in the\nvertex operator construction are provided by the Heisenberg subalgebras of\n$SL(M+K+1)$ realized in the unconventional gradations. The well-known limiting\ncases are the homogeneous Heisenberg subalgebra of $SL(M+1)$ and the principal\nHeisenberg subalgebra of ${\\hat{sl}}(K+1)$. The explicit example of $M=K=1$ is\ndiscussed in detail and the corresponding soliton solutions and tau-functions\nare given.",
    "arxiv_id": "solv-int/9711011",
    "authors": [
      "H. Aratyn",
      "L. A. Ferreira",
      "J. F. Gomes",
      "A. H. Zimerman"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1007/BFb0105320",
    "title": "Vertex Operators and Solitons of Constrained KP Hierarchies",
    "url": "https://arxiv.org/abs/solv-int/9711011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2628ec10-8a7e-40ca-8aba-ce5a00353735",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}