{
  "id": "1410.0435",
  "version": "v1",
  "published": "2014-10-02T02:02:18.000Z",
  "updated": "2014-10-02T02:02:18.000Z",
  "title": "Stacks in Representation Theory. What is a continuous representation of an algebraic group ?",
  "authors": [
    "Joseph Bernstein"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of view necessarily leads to a conclusion that the standard approach to (continuous) representations of algebraic groups is ideologically inconsistent. I propose a way to modify this approach using sheaves on stacks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-02T02:02:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation theory",
      "algebraic group",
      "continuous representation",
      "geometric object",
      "standard approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0435B"
    }
  }
}