{
  "id": "0905.0065",
  "version": "v3",
  "published": "2009-05-01T08:50:25.000Z",
  "updated": "2010-06-29T10:01:47.000Z",
  "title": "Complete Reducibility and Conjugacy classes of tuples in Algebraic Groups and Lie algebras",
  "authors": [
    "M. Bate",
    "B. Martin",
    "G. Roehrle",
    "R. Tange"
  ],
  "comment": "23 pages; final version to appear in Math. Z; various changes following suggestion by the referee",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G^n, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in G^n, generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalization of Serre's notion of G-complete reducibility. This concept appears to be new, even in characteristic zero. We discuss how to extend some key results on G-complete reducibility in this framework. We also consider some rationality questions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-06-29T10:01:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G15",
      "14L24",
      "20E42"
    ],
    "keywords": [
      "algebraic groups",
      "conjugacy classes",
      "lie algebras",
      "g-complete reducibility",
      "n-fold cartesian product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0065B"
    }
  }
}