{
  "id": "2107.06220",
  "version": "v1",
  "published": "2021-07-13T16:21:07.000Z",
  "updated": "2021-07-13T16:21:07.000Z",
  "title": "Lattice associated to a Shi variety",
  "authors": [
    "Nathan Chapelier-Laget"
  ],
  "comment": "14 pages, 9 figures",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Let $W$ be a irreducible Weyl group and $W_a$ its affine Weyl group. In a previous article the author defined an affine variety $\\widehat{X}_{W_a}$, called the Shi variety of $W_a$, whose integral points are in bijection with $W_a$. The set of irreducible components of $\\widehat{X}_{W_a}$, denoted $H^0(\\widehat{X}_{W_a})$, is of some interest and we show in this article that $H^0(\\widehat{X}_{W_a})$ has a structure of semidistributive lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-13T16:21:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shi variety",
      "affine weyl group",
      "integral points",
      "irreducible weyl group",
      "affine variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}