{
  "id": "1901.02336",
  "version": "v1",
  "published": "2019-01-08T14:57:19.000Z",
  "updated": "2019-01-08T14:57:19.000Z",
  "title": "On Soergel bimodules",
  "authors": [
    "Noriyuki Abe"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a Coxeter system and its representation $V$, Soergel defined a category which is now called the category of Soergel bimodules and proved that this gives a categorification of the Hecke algebra when $V$ is reflection faithful. Elias and Williamson defined another category which is equivalent to the category of Soergel bimodules when $V$ is reflection faithful. Moreover they proved the categorification theorem for their category with less assumptions on $V$. In this paper, we give a `bimodule theoretic' definition of the category of Elias-Williamson and reprove the categorification theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-08T14:57:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55"
    ],
    "keywords": [
      "soergel bimodules",
      "categorification theorem",
      "coxeter system",
      "bimodule theoretic",
      "hecke algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}