{
  "id": "1601.03426",
  "version": "v1",
  "published": "2016-01-13T22:07:32.000Z",
  "updated": "2016-01-13T22:07:32.000Z",
  "title": "Deligne categories as limits in rank and characteristic",
  "authors": [
    "Nate Harman"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give new interpretations of the Deligne categories $\\underline{Rep}(GL_t)$ and $\\underline{Rep}(S_t)$ (and their abelian envelopes) over $\\mathbb{C}$ in terms of modular representations of general linear and symmetric groups of large rank in large characteristic. In particular we make sense of the sentence \"$\\underline{Rep}(S_n)$ is the limit of $Rep(S_{p+n})$ over $\\bar{\\mathbb{F}}_p$ as $p$ goes to infinity\". We then give examples of how to pass results between these different settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-13T22:07:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deligne categories",
      "general linear",
      "modular representations",
      "symmetric groups",
      "large rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103426H"
    }
  }
}