{
  "id": "hep-th/9210117",
  "version": "v1",
  "published": "1992-10-21T21:40:25.000Z",
  "updated": "1992-10-21T21:40:25.000Z",
  "title": "On the KP Hierarchy, $\\hat{W}_{\\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model: I. The Classical Case",
  "authors": [
    "Feng Yu",
    "Yong-Shi Wu"
  ],
  "comment": "29p",
  "journal": "J.Math.Phys. 34 (1993) 5851-5871",
  "doi": "10.1063/1.530286",
  "categories": [
    "hep-th"
  ],
  "abstract": "In this paper we study the inter-relationship between the integrable KP hierarchy, nonlinear $\\hat{W}_{\\infty}$ algebra and conformal noncompact $SL(2,R)/U(1)$ coset model at the classical level. We first derive explicitly the Possion brackets of the second Hamiltonian structure of the KP hierarchy, then use it to define the $\\hat{W}_{1+\\infty}$ algebra and its reduction $\\hat{W}_{\\infty}$. Then we show that the latter is realized in the $SL(2,R)/U(1)$ coset model as a hidden current algebra, through a free field realization of $\\hat{W}_{\\infty}$, in closed form for all higher-spin currents, in terms of two bosons. An immediate consequence is the existence of an infinite number of KP flows in the coset model, which preserve the $\\hat{W}_{\\infty}$ current algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-10-21T21:40:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal sl",
      "classical case",
      "coset model",
      "free field realization",
      "hidden current algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 339392
    }
  }
}