{
  "id": "1607.03271",
  "version": "v1",
  "published": "2016-07-12T09:02:48.000Z",
  "updated": "2016-07-12T09:02:48.000Z",
  "title": "Relative hard Lefschetz for Soergel bimodules",
  "authors": [
    "Ben Elias",
    "Geordie Williamson"
  ],
  "comment": "29 pages, preliminary version",
  "categories": [
    "math.RT",
    "math.AG",
    "math.QA"
  ],
  "abstract": "We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category associated by Lusztig to any 2-sided cell in a Coxeter group is rigid and pivotal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-12T09:02:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "soergel bimodules",
      "relative hard lefschetz theorem implies",
      "kazhdan-lusztig basis",
      "structure constants",
      "tensor category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}