{
  "id": "0808.2998",
  "version": "v2",
  "published": "2008-08-21T20:57:24.000Z",
  "updated": "2018-05-24T11:38:28.000Z",
  "title": "Nilpotent orbits in the dual of classical Lie algebras in characteristic 2 and the Springer correspondence",
  "authors": [
    "Ting Xue"
  ],
  "comment": "26 pages. arXiv admin note: text overlap with arXiv:0808.2995",
  "journal": "Represent. Theory 13 (2009), 609--635",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we classify the nilpotent orbits in the duals of symplectic and orthogonal Lie algebras over algebraically closed or finite fields of characteristic 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-21T20:57:24.000Z",
      "abstract": "We classify the nilpotent orbits in the dual space of the classical Lie algebras over an algebraically closed field or a finite field of characteristic 2. In particular, we obtain the number of nilpotent orbits over $\\tF_{2^n}$. We also give the structure of the component groups of centralizers. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the dual space of the Lie algebra of $G$.",
      "comment": "19 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-05-24T11:38:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical lie algebras",
      "nilpotent orbits",
      "springer correspondence",
      "characteristic",
      "dual space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2998X"
    }
  }
}