{
  "id": "0805.1147",
  "version": "v1",
  "published": "2008-05-08T11:39:01.000Z",
  "updated": "2008-05-08T11:39:01.000Z",
  "title": "A cellular algebra with certain idempotent decomposition",
  "authors": [
    "Kentaro Wada"
  ],
  "comment": "37pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a cellular algebra $\\A$ with a cellular basis $\\ZC$, we consider a decomposition of the unit element $1_\\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis $\\ZC$ can be partitioned into some pieces with good properties. Then by using a certain map $\\a$, we give a coarse partition of $\\ZC$ whose refinement is the original partition. We construct a Levi type subalgebra $\\aA$ of $\\A$ and its quotient algebra $\\oA$, and also construct a parabolic type subalgebra $\\tA$ of $\\A$, which contains $\\aA$ with respect to the map $\\a$. Then, we study the relation of standard modules, simple modules and decomposition numbers among these algebras. Finally, we study the relationship of blocks among these algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-08T11:39:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "20C20",
      "20G05"
    ],
    "keywords": [
      "cellular algebra",
      "idempotent decomposition",
      "cellular basis",
      "parabolic type subalgebra",
      "levi type subalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1147W"
    }
  }
}