{
  "id": "2312.14827",
  "version": "v1",
  "published": "2023-12-22T16:59:14.000Z",
  "updated": "2023-12-22T16:59:14.000Z",
  "title": "On the smooth locus of affine Schubert varieties",
  "authors": [
    "Georgios Pappas",
    "Rong Zhou"
  ],
  "comment": "16 pages. Comments welcome!",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We give a simple and uniform proof of a conjecture of Haines-Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-22T16:59:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine schubert varieties",
      "smooth locus",
      "representation theoretic techniques",
      "combinatorial analysis",
      "uniform proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}