{
  "id": "1801.09599",
  "version": "v1",
  "published": "2018-01-29T16:08:42.000Z",
  "updated": "2018-01-29T16:08:42.000Z",
  "title": "A Partial Order on Bipartions From the Generalized Springer Correspondence",
  "authors": [
    "Jianqiao Xia"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In \\cite{Lusztig}, Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set $\\mathcal{N}$ of unipotent classes in a spin group which carry irreducible local systems equivariant for the spin group but not equivariant for the special orthogonal group. The set $\\mathcal{N}$ has a natural partial order and therefore induces a partial order on bipartitions. We use the explicit formula given in \\cite{Lusztig} to prove that this partial order on bipartitions is the same as the dominance order given by Geck and Iancu, in \\cite{Iancu}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-29T16:08:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized springer correspondence",
      "bipartions",
      "spin group",
      "carry irreducible local systems equivariant",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}