{
  "id": "math/0610896",
  "version": "v2",
  "published": "2006-10-29T15:20:06.000Z",
  "updated": "2008-03-26T22:54:21.000Z",
  "title": "Constructing irreducible representations of quantum groups $U_{q}(f_{m}(K))$",
  "authors": [
    "Xin Tang"
  ],
  "comment": "19 pages, some modifications made to the first version",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we construct families of irreducible representations for a class of quantum groups $U_{q}(f_{m}(K))$. First, we give a natural construction of irreducible weight representations for $U_{q}(f_{m}(K))$ using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of $U_{q}(f_{m}(K))$. As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-26T22:54:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "16B30",
      "16B35"
    ],
    "keywords": [
      "quantum groups",
      "constructing irreducible representations",
      "natural construction",
      "irreducible weight representations",
      "construct families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10896T"
    }
  }
}