{
  "id": "2208.14058",
  "version": "v1",
  "published": "2022-08-30T08:19:19.000Z",
  "updated": "2022-08-30T08:19:19.000Z",
  "title": "Affine Deligne--Lusztig varieties with finite Coxeter parts",
  "authors": [
    "Xuhua He",
    "Sian Nie",
    "Qingchao Yu"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT",
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this paper, we study affine Deligne--Lusztig varieties $X_w(b)$ when the finite part of the element $w$ in the Iwahori--Weyl group is a partial $\\sigma$-Coxeter element. We show that such $w$ is a cordial element and $X_w(b) \\neq \\emptyset$ if and only if $b$ satisfies a certain Hodge--Newton indecomposability condition. The main result of this paper is that for such $w$ and $b$, $X_w(b)$ has a simple geometric structure: the $\\sigma$-centralizer of $b$ acts transitively on the set of irreducible components of $X_w(b)$; and each irreducible component is an iterated fibration over a classical Deligne--Lusztig variety of Coxeter type, and the iterated fibers are either $\\mathbb A^1$ or $\\mathbb G_m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T08:19:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G25",
      "20G25"
    ],
    "keywords": [
      "finite coxeter parts",
      "study affine deligne-lusztig varieties",
      "hodge-newton indecomposability condition",
      "simple geometric structure",
      "irreducible component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}