{
  "id": "1507.00970",
  "version": "v1",
  "published": "2015-07-03T17:17:43.000Z",
  "updated": "2015-07-03T17:17:43.000Z",
  "title": "On support varieties and the Humphreys conjecture in type $A$",
  "authors": [
    "William D. Hardesty"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a reductive algebraic group scheme defined over $\\mathbb{F}_p$ and let $G_1$ denote the Frobenius kernel of $G$. To each finite-dimensional $G$-module $M$, one can define the support variety $V_{G_1}(M)$, which can be regarded as a $G$-stable closed subvariety of the nilpotent cone. A $G$-module is called a tilting module if it has both good and Weyl filtrations. In 1997, it was conjectured by J.E. Humphreys that when $p\\geq h$, the support varieties of the indecomposable tilting modules coincide with the nilpotent orbits given by the Lusztig bijection. In this paper, we shall verify this conjecture when $G=SL_n$ and $p > n+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-03T17:17:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "support variety",
      "humphreys conjecture",
      "reductive algebraic group scheme",
      "frobenius kernel",
      "lusztig bijection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150700970H"
    }
  }
}