{
  "id": "0904.2734",
  "version": "v1",
  "published": "2009-04-17T16:01:29.000Z",
  "updated": "2009-04-17T16:01:29.000Z",
  "title": "The category $\\mathcal{O}$ for a general Coxeter system",
  "authors": [
    "Noriyuki Abe"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the category $\\mathcal{O}$ for a general Coxeter system using a formulation of Fiebig. The translation functors, the Zuckerman functors and the twisting functors are defined. We prove the fundamental properties of these functors, the duality of Zuckerman functor and generalization of Verma's result about homomorphisms between Verma modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-17T16:01:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "17B10"
    ],
    "keywords": [
      "general coxeter system",
      "zuckerman functor",
      "fundamental properties",
      "verma modules",
      "translation functors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2734A"
    }
  }
}