{
  "id": "1602.04314",
  "version": "v1",
  "published": "2016-02-13T10:48:57.000Z",
  "updated": "2016-02-13T10:48:57.000Z",
  "title": "Simple transitive 2-representations for some 2-subcategories of Soergel bimodules",
  "authors": [
    "Marco Mackaay",
    "Volodymyr Mazorchuk"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We classify simple transitive $2$-representations of certain $2$-sub\\-ca\\-te\\-go\\-ri\\-es of the $2$-category of Soergel bimodules over the coinvariant algebra in Coxeter types $B_2$ and $I_2(5)$. In the $I_2(5)$ case it turns out that simple transitive $2$-representations are exhausted by cell $2$-representations. In the $B_2$ case we show that, apart from cell $2$-representations, there is a unique, up to equivalence, additional simple transitive $2$-representation and we give an explicit construction of this $2$-representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-13T10:48:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "soergel bimodules",
      "representation",
      "coinvariant algebra",
      "explicit construction",
      "coxeter types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204314M"
    }
  }
}