{
  "id": "1702.07570",
  "version": "v1",
  "published": "2017-02-24T13:26:04.000Z",
  "updated": "2017-02-24T13:26:04.000Z",
  "title": "Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions",
  "authors": [
    "Christof Geiß",
    "Bernard Leclerc",
    "Jan Schröer"
  ],
  "comment": "49 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of generalized preprojective algebras. Conjecturally these functions yield semicanonical bases of the enveloping algebras of the positive part of symmetrizable Kac-Moody algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-24T13:26:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetrizable cartan matrices",
      "crystal graphs",
      "semicanonical functions",
      "functions yield semicanonical bases",
      "generalize lusztigs nilpotent varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}