{
  "id": "0908.2739",
  "version": "v1",
  "published": "2009-08-19T12:55:03.000Z",
  "updated": "2009-08-19T12:55:03.000Z",
  "title": "Translation for finite W-algebras",
  "authors": [
    "Simon M. Goodwin"
  ],
  "comment": "38 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "A finite $W$-algebra $U(\\g,e)$ is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\\g$. It is possible to give the tensor product of a $U(\\g,e)$-module with a finite dimensional $U(\\g)$-module the structure of a $U(\\g,e)$-module; we refer to such tensor products as translations. In this paper, we present a number of fundamental properties of these translations, which are expected to be of importance in understanding the representation theory of $U(\\g,e)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-19T12:55:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B35",
      "81R05"
    ],
    "keywords": [
      "finite w-algebras",
      "translation",
      "tensor product",
      "complex reductive lie algebra",
      "nilpotent element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2739G"
    }
  }
}