{
  "id": "1904.01884",
  "version": "v1",
  "published": "2019-04-03T09:54:12.000Z",
  "updated": "2019-04-03T09:54:12.000Z",
  "title": "Projection of root systems",
  "authors": [
    "Sarah Dijols"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $a$ be a real euclidean vector space of finite dimension and $\\Sigma$ a root system in $a$ with a basis $\\Delta$. Let $\\Theta \\subset \\Delta$ and $M = M_{\\Theta}$ be a standard Levi of a reductive group $G$ such that $a_{\\Theta} = a_M\\slash a_G$. Let us denote $d$ the dimension of $a_{\\Theta}$, i.e the cardinal of $\\Delta - \\Theta$ and $\\Sigma_{\\Theta}$ the set of all non-trivial projections of roots in $\\Sigma$. We obtain conditions on $\\Theta$ such that $\\Sigma_{\\Theta}$ contains a root system of rank $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T09:54:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "root system",
      "real euclidean vector space",
      "finite dimension",
      "standard levi",
      "non-trivial projections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}