{
  "id": "math/0703528",
  "version": "v2",
  "published": "2007-03-18T20:43:00.000Z",
  "updated": "2007-11-17T00:40:28.000Z",
  "title": "Filtrations in Modular Representations of Reductive Lie Algebras",
  "authors": [
    "Yiyang Li",
    "Bin Shu"
  ],
  "comment": "The current version of this paper will appear in Algebra Colloquium",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive algebraic group $G$ over an algebraically closed field $k$ of prime characteristic $p$, and $\\ggg=\\Lie(G)$. In this paper, we study modular representations of the reductive Lie algebra $\\ggg$ with $p$-character $\\chi$ of standard Levi-form associated with an index subset $I$ of simple roots. With aid of support variety theory we prove a theorem that a $U_\\chi(\\ggg)$-module is projective if and only if it is a strong \"tilting\" module, i.e. admitting both $\\cz_Q$- and $\\cz^{w^I}_Q$-filtrations (to see Theorem \\ref{THMFORINV}). Then by analogy of the arguments in \\cite{AK} for $G_1T$-modules, we construct so-called Andersen-Kaneda filtrations associated with each projective $\\ggg$-module of $p$-character $\\chi$, and finally obtain sum formulas from those filtrations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-17T00:40:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B20",
      "17B35",
      "17B50"
    ],
    "keywords": [
      "reductive lie algebra",
      "filtrations",
      "study modular representations",
      "support variety theory",
      "standard levi-form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3528L"
    }
  }
}