{
  "id": "math/0210408",
  "version": "v4",
  "published": "2002-10-26T16:42:13.000Z",
  "updated": "2004-04-18T15:24:11.000Z",
  "title": "Representations of finite groups on Riemann-Roch spaces",
  "authors": [
    "David Joyner",
    "Will Traves"
  ],
  "comment": "24 pages, significant revision",
  "categories": [
    "math.AG",
    "cs.IT",
    "math.GR",
    "math.IT"
  ],
  "abstract": "We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$ left stable by $G$ then we show the irreducible constituents of the natural representation of $G$ on the Riemann-Roch space $L(D)=L_X(D)$ are of dimension $\\leq d$, where $d$ is the size of the smallest $G$-orbit acting on $X$. We give an example to show that this is, in general, sharp (i.e., that dimension $d$ irreducible constituents can occur). Connections with coding theory, in particular to permutation decoding of AG codes, are discussed in the last section. Many examples are included.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-04-18T15:24:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37",
      "20C20",
      "94B27",
      "11T71",
      "05E20"
    ],
    "keywords": [
      "riemann-roch space",
      "finite group",
      "irreducible constituents",
      "automorphism group",
      "natural representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10408J"
    }
  }
}