{
  "id": "math/0201104",
  "version": "v3",
  "published": "2002-01-11T20:24:53.000Z",
  "updated": "2003-10-13T22:49:22.000Z",
  "title": "Bruhat order for two flags and a line",
  "authors": [
    "Peter Magyar"
  ],
  "comment": "36 pages. Version 2 adds an Introduction stating results in terms of S_n; and corrects typos, including in statement of move (v). Version 3: typos",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a linear space V under linear transformations of V; or equivalently, it describes the closure of an orbit of GL(V) acting diagonally on the product of two flag varieties. We consider the degenerations of a triple consisting of two flags and a line, or equivalently the closure of an orbit of GL(V) acting diagonally on the product of two flag varieties and a projective space. We give a simple rank criterion to decide whether one triple can degenerate to another. We also classify the minimal degenerations, which involve not only reflections (i.e., transpositions) in the Weyl group S_n, n=dim(V), but also cycles of arbitrary length. Our proofs use only elementary linear algebra and combinatorics.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-10-13T22:49:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L35",
      "51N30"
    ],
    "keywords": [
      "flag varieties",
      "simple rank criterion",
      "elementary linear algebra",
      "linear space",
      "classical ehresmann-bruhat order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1104M"
    }
  }
}