{
  "id": "1503.08279",
  "version": "v1",
  "published": "2015-03-28T07:59:23.000Z",
  "updated": "2015-03-28T07:59:23.000Z",
  "title": "SO(2n,C)-character varieties are not varieties of characters",
  "authors": [
    "Adam S. Sikora"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that the coordinate rings of SO(2n,C)-character varieties are not generated by trace functions nor generalized trace functions for $n\\geq 2$ and all groups Gamma of corank $\\geq 2.$ Furthermore, we give examples of non-conjugate completely reducible representations undistinguishable by generalized trace functions. Hence, SO(2n,C)-character varieties are not varieties of characters! However, we also prove that any generic SO(2n,C)-representation of a free group can be distinguished from all non-equivalent representations by trace functions and by a single generalized trace function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-28T07:59:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "20C15",
      "13A50",
      "14L24"
    ],
    "keywords": [
      "characters",
      "single generalized trace function",
      "free group",
      "groups gamma",
      "non-equivalent representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150308279S"
    }
  }
}