{
  "id": "0708.2138",
  "version": "v1",
  "published": "2007-08-16T05:41:41.000Z",
  "updated": "2007-08-16T05:41:41.000Z",
  "title": "Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups",
  "authors": [
    "S. S. Kannan",
    "Pranab Sardar"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$ modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to the ample generator of the Picard group of $G_{2,n}$. We also prove that the flag variety $GL_{n}(k)/B_{n}$ can be obtained as a GIT quotient of $GL_{n+1}(k)/B_{n+1}$ modulo a maximal torus of $SL_{n+1}(k)$ for a suitable choice of an ample line bundle on $GL_{n+1}(k)/B_{n+1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-16T05:41:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Lxx"
    ],
    "keywords": [
      "general linear group",
      "symmetric groups",
      "torus quotients",
      "standard representation",
      "homogeneous spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2138K"
    }
  }
}