{
  "id": "2302.09329",
  "version": "v1",
  "published": "2023-02-18T13:31:17.000Z",
  "updated": "2023-02-18T13:31:17.000Z",
  "title": "Zigzag algebras and faithfulness of the 2-braid groups in type B",
  "authors": [
    "Edmund Heng",
    "Kie Seng Nge"
  ],
  "comment": "15 pages. Split from an earlier paper following referee suggestion. Comments welcomed!",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We show that certain category of bimodules over a finite dimensional quiver algebra known as type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier's conjecture on the faithfulness of the 2-braid groups for type B.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-18T13:31:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20J05",
      "20C08"
    ],
    "keywords": [
      "zigzag algebra",
      "faithfulness",
      "finite dimensional quiver algebra",
      "quotient category",
      "soergel bimodules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}