{
  "id": "0711.3353",
  "version": "v2",
  "published": "2007-11-21T11:41:32.000Z",
  "updated": "2008-07-29T17:42:52.000Z",
  "title": "On orbits of antichains of positive roots",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "12 pages, final version; to appear in Europ. J. Combinatorics",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "For any finite poset P, there is a natural operator $X$ acting on the antichains of P. We discuss conjectural properties of this operator for some graded posets associated with irreducible root systems. In particular, if $\\Delta^+$ is the set of positive roots and $\\Pi$ is the set of simple roots in $\\Delta^+$, then we consider the cases $P=\\Delta^+$ and $\\Delta^+\\setminus \\Pi$. For the root system of type $A_n$, we consider an $X$-invariant integer-valued function on the set of antichains of $\\Delta^+$ and establish some properties of it.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-29T17:42:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive roots",
      "antichains",
      "conjectural properties",
      "invariant integer-valued function",
      "finite poset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3353P"
    }
  }
}