{
  "id": "0907.0031",
  "version": "v1",
  "published": "2009-06-30T21:50:57.000Z",
  "updated": "2009-06-30T21:50:57.000Z",
  "title": "New bases of some Hecke algebras via Soergel bimodules",
  "authors": [
    "Nicolas Libedinsky"
  ],
  "comment": "25 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "For extra-large Coxeter systems (m(s,r)>3), we construct a natural and explicit set of Soergel bimodules D={D_w}_{w\\in W} such that each D_w contains as a direct summand (or is equal to) the indecomposable Soergel bimodule B_w. When decategorified, we prove that D gives rise to a set {d_w}_{w\\in W} that is actually a basis of the Hecke algebra. This basis is close to the Kazhdan-Lusztig basis and satisfies a ``positivity condition''.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-30T21:50:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke algebra",
      "extra-large coxeter systems",
      "direct summand",
      "indecomposable soergel bimodule",
      "explicit set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0031L"
    }
  }
}