{
  "id": "1709.06589",
  "version": "v1",
  "published": "2017-09-19T18:15:51.000Z",
  "updated": "2017-09-19T18:15:51.000Z",
  "title": "On the definition of Heisenberg category",
  "authors": [
    "Jonathan Brundan"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We revisit the definition of the Heisenberg category of level k. In level -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. In other negative levels, the definition is due to Mackaay and Savage, also with some redundant relations, while the level zero case is the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T18:15:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "18D10"
    ],
    "keywords": [
      "heisenberg category",
      "definition",
      "additional cyclicity relations",
      "affine oriented brauer category",
      "level zero case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}