{
  "id": "1708.06536",
  "version": "v1",
  "published": "2017-08-22T08:43:02.000Z",
  "updated": "2017-08-22T08:43:02.000Z",
  "title": "Minimal W-superalgebras and modular representations of basic Lie superalgebras",
  "authors": [
    "Yang Zeng",
    "Bin Shu"
  ],
  "comment": "57 pages, any comments are welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $\\mathfrak{g}=\\mathfrak{g}_{\\bar 0}+\\mathfrak{g}_{\\bar 1}$ be a basic Lie superalgebra over $\\mathbb{C}$, and $e$ a minimal nilpotent element in $\\mathfrak{g}_{\\bar 0}$. Set $W_\\chi'$ to be the refined $W$-superalgebra associated with the pair $(\\mathfrak{g},e)$, which is called a minimal $W$-superalgebra. In this paper we present a set of explicit generators of minimal $W$-superalgebras and the commutators between them. In virtue of this, we show that over an algebraically closed field $\\mathds{k}$ of characteristic $p\\gg0$, the lower bounds of dimensions in the modular representations of basic Lie superalgebras with minimal nilpotent $p$-characters are attainable. Such lower bounds are indicated in \\cite{WZ} as the super Kac-Weisfeiler property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-22T08:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "basic lie superalgebra",
      "modular representations",
      "minimal w-superalgebras",
      "lower bounds",
      "minimal nilpotent element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}