{
  "id": "1208.2380",
  "version": "v4",
  "published": "2012-08-11T19:10:44.000Z",
  "updated": "2016-06-13T10:52:18.000Z",
  "title": "Character correspondences for symmetric groups and wreath products",
  "authors": [
    "Anton Evseev"
  ],
  "comment": "Proof of Theorem 4.8 simplified. To appear in Forum Math",
  "categories": [
    "math.RT"
  ],
  "abstract": "The Alperin--McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its $p$-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this refinement holds for all blocks of symmetric groups. Along the way we identify a \"canonical\" isometry between the principal block of $S_{pw}$ and that of $S_p\\wr S_w$. We also prove a general theorem on expressing virtual characters of wreath products in terms of certain induced characters. Much of the paper generalises character-theoretic results on blocks of symmetric groups with abelian defect and related wreath products to the case of arbitrary defect.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-03T14:12:52.000Z",
      "comment": "Proof of Lemma 5.14 corrected; some changes made to Section 7; minor changes/corrections elsewhere",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-06-13T10:52:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric groups",
      "character correspondences",
      "paper generalises character-theoretic results",
      "alperin-mckay conjecture relates irreducible characters",
      "arbitrary finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2380E"
    }
  }
}