{
  "id": "1404.6879",
  "version": "v1",
  "published": "2014-04-28T06:55:40.000Z",
  "updated": "2014-04-28T06:55:40.000Z",
  "title": "Quantization of the shift of argument subalgebras in type A",
  "authors": [
    "Vyacheslav Futorny",
    "Alexander Molev"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a simple Lie algebra $\\mathfrak{g}$ and an element $\\mu\\in\\mathfrak{g}^*$, the corresponding shift of argument subalgebra of $\\text{S}(\\mathfrak{g})$ is Poisson commutative. In the case where $\\mu$ is regular, this subalgebra is known to admit a quantization, that is, it can be lifted to a commutative subalgebra of $\\text{U}(\\mathfrak{g})$. We show that if $\\mathfrak{g}$ is of type $A$, then this property extends to arbitrary $\\mu$, thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof relies on an explicit construction of generators of the center of the affine vertex algebra at the critical level.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-28T06:55:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "argument subalgebra",
      "quantization",
      "simple lie algebra",
      "affine vertex algebra",
      "toledano laredo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.6879F"
    }
  }
}