{
  "id": "1111.5811",
  "version": "v3",
  "published": "2011-11-24T16:21:20.000Z",
  "updated": "2014-09-24T10:55:19.000Z",
  "title": "Decomposition of Tensor Products of Modular Irreducible Representations for $SL_3$: the $p \\geq 5$ case",
  "authors": [
    "C. Bowman",
    "S. R. Doty",
    "S. Martin"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the structure of the indecomposable direct summands of tensor products of two restricted simple $SL_3(K)$-modules, where $K$ is an algebraically closed field of characteristic $p \\geq 5$. We give a characteristic-free algorithm for the computation of the decomposition of such a tensor product into indecomposable modules. The $p<5$ case for $\\SL_3(K)$ was studied in the authors' earlier paper. In this paper we show that for characteristics $p\\geq 5$ all the indecomposable summands are rigid, in contrast to the situation in characteristic 3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-10T08:23:06.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-24T10:55:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tensor product",
      "modular irreducible representations",
      "decomposition",
      "indecomposable direct summands",
      "characteristic-free algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5811B"
    }
  }
}