{
  "id": "1510.01556",
  "version": "v1",
  "published": "2015-10-06T12:44:39.000Z",
  "updated": "2015-10-06T12:44:39.000Z",
  "title": "The $p$-Canonical Basis for Hecke Algebras",
  "authors": [
    "Lars Thorge Jensen",
    "Geordie Williamson"
  ],
  "comment": "32 pages, many TikZ pictures, best viewed in colour and pdf",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We describe a positive characteristic analogue of the Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic Coxeter system and investigate some of its properties. Using Soergel calculus we describe an algorithm to calculate this basis. We outline some known or expected applications in modular representation theory. We conclude by giving several examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-06T12:44:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke algebra",
      "canonical basis",
      "modular representation theory",
      "crystallographic coxeter system",
      "soergel calculus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151001556T"
    }
  }
}