{
  "id": "0704.3061",
  "version": "v1",
  "published": "2007-04-23T18:59:56.000Z",
  "updated": "2007-04-23T18:59:56.000Z",
  "title": "Bruhat order for two subspaces and a flag",
  "authors": [
    "Evgeny Smirnov"
  ],
  "comment": "30 pages, with figures",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a finite-dimensional vector space V; or, equivalently, the closure of an orbit of the group GL(V) acting on the direct product of two full flag varieties. We obtain a similar result for triples consisting of two subspaces and a partial flag in V; this is equivalent to describing the closure of a GL(V)-orbit in the product of two Grassmannians and one flag variety. We give a rank criterion to check whether such a triple can be degenerated to another one, and we classify the minimal degenerations. Our methods involve only elementary linear algebra and combinatorics of graphs (originating in Auslander-Reiten quivers).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-23T18:59:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L35",
      "16G70"
    ],
    "keywords": [
      "flag variety",
      "finite-dimensional vector space",
      "full flag varieties",
      "elementary linear algebra",
      "group gl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3061S"
    }
  }
}