{
  "id": "math/0403095",
  "version": "v2",
  "published": "2004-03-04T15:15:54.000Z",
  "updated": "2004-10-14T11:46:15.000Z",
  "title": "Fixed points of involutive automorphisms of the Bruhat order",
  "authors": [
    "Axel Hultman"
  ],
  "comment": "16 pages. Appendix added, minor revisions; to appear in Adv. Math",
  "categories": [
    "math.CO"
  ],
  "abstract": "Applying a classical theorem of Smith, we show that the poset property of being Gorenstein$^*$ over $\\mathbb{Z}_2$ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. Incitti. We also show that the Bruhat order on the fixed points of an involutive automorphism induced by a Coxeter graph automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as a Coxeter group in its own right.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-14T11:46:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bruhat order",
      "fixed points",
      "involutive automorphism",
      "arbitrary coxeter group",
      "coxeter graph automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3095H"
    }
  }
}