{
  "id": "1911.08645",
  "version": "v1",
  "published": "2019-11-20T00:45:25.000Z",
  "updated": "2019-11-20T00:45:25.000Z",
  "title": "Classical W-algebras for centralizers",
  "authors": [
    "A. I. Molev",
    "E. Ragoucy"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a new family of Poisson vertex algebras $\\mathcal{W}(\\mathfrak{a})$ analogous to the classical $\\mathcal{W}$-algebras. The algebra $\\mathcal{W}(\\mathfrak{a})$ is associated with the centralizer $\\mathfrak{a}$ of an arbitrary nilpotent element in $\\mathfrak{gl}_N$. We show that $\\mathcal{W}(\\mathfrak{a})$ is an algebra of polynomials in infinitely many variables and produce its free generators in an explicit form. This implies that $\\mathcal{W}(\\mathfrak{a})$ is isomorphic to the center at the critical level of the affine vertex algebra associated with $\\mathfrak{a}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-20T00:45:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical w-algebras",
      "centralizer",
      "poisson vertex algebras",
      "arbitrary nilpotent element",
      "affine vertex algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}