{
  "id": "math/0606460",
  "version": "v2",
  "published": "2006-06-19T14:29:34.000Z",
  "updated": "2006-09-05T19:31:54.000Z",
  "title": "Parities of v-decomposition numbers and an application to symmetric group algebras",
  "authors": [
    "Kai Meng Tan"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We prove that the v-decomposition number $d_{\\lambda\\mu}(v)$ is an even or odd polynomial according to whether the partitions $\\lambda$ and $\\mu$ have the same relative sign (or parity) or not. We then use this result to verify Martin's conjecture for weight 3 blocks of symmetric group algebras -- that these blocks have the property that their projective (indecomposable) modules have a common radical length 7.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-05T19:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "20C30"
    ],
    "keywords": [
      "symmetric group algebras",
      "v-decomposition number",
      "application",
      "odd polynomial",
      "verify martins conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6460M"
    }
  }
}