{
  "id": "1011.2431",
  "version": "v4",
  "published": "2010-11-10T16:59:19.000Z",
  "updated": "2015-06-26T09:52:36.000Z",
  "title": "Conjugacy classes in Weyl groups and q-W algebras",
  "authors": [
    "A. Sevostyanov"
  ],
  "comment": "48 pages; some arguments in the proof of Proposition 12.2 are clarified",
  "categories": [
    "math.RT",
    "hep-th",
    "math.QA"
  ],
  "abstract": "We define noncommutative deformations $W_q^s(G)$ of algebras of functions on certain (finite coverings of) transversal slices to the set of conjugacy classes in an algebraic group $G$ which play the role of Slodowy slices in algebraic group theory. The algebras $W_q^s(G)$ called q-W algebras are labeled by (conjugacy classes of) elements $s$ of the Weyl group of $G$. The algebra $W_q^s(G)$ is a quantization of a Poisson structure defined on the corresponding transversal slice in $G$ with the help of Poisson reduction of a Poisson bracket associated to a Poisson-Lie group $G^*$ dual to a quasitriangular Poisson-Lie group. The algebras $W_q^s(G)$ can be regarded as quantum group counterparts of W-algebras. However, in general they are not deformations of the usual W-algebras.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-30T13:42:32.000Z",
      "comment": "48 pages; some proofs improved; misprints corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-06-26T09:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "17B63",
      "20F55",
      "20G20"
    ],
    "keywords": [
      "conjugacy classes",
      "q-w algebras",
      "weyl group",
      "transversal slice",
      "quasitriangular poisson-lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 876685,
      "adsabs": "2010arXiv1011.2431S"
    }
  }
}