{
  "id": "1306.4290",
  "version": "v2",
  "published": "2013-06-18T18:37:43.000Z",
  "updated": "2013-06-20T20:48:35.000Z",
  "title": "Modular representations of Heisenberg algebras",
  "authors": [
    "Fernando Szechtman"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $F$ be be an arbitrary field and let $h(n)$ be the Heisenberg algebra of dimension $2n+1$ over $F$. It was shown by Burde that if $F$ has characteristic 0 then the minimum dimension of a faithful $h(n)$-module is $n+2$. We show here that his result remains valid in prime characteristic $p$, as long as $(p,n)\\neq (2,1)$. We construct, as well, various families of faithful irreducible $h(n)$-modules if $F$ has prime characteristic, and classify these when $F$ is algebraically closed. Applications to matrix theory are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-20T20:48:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "heisenberg algebra",
      "modular representations",
      "prime characteristic",
      "result remains valid",
      "matrix theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.4290S"
    }
  }
}