{
  "id": "1907.06579",
  "version": "v1",
  "published": "2019-07-15T16:37:40.000Z",
  "updated": "2019-07-15T16:37:40.000Z",
  "title": "Tilting modules for classical Lie superalgebras",
  "authors": [
    "Chih-Whi Chen",
    "Shun-Jen Cheng",
    "Kevin Coulembier"
  ],
  "comment": "32 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study tilting and projective-injective modules in a parabolic BGG category $\\mathcal O$ for an arbitrary classical Lie superalgebra. We establish a version of Ringel duality for this type of Lie superalgebras which allows to express the characters of tilting modules in terms of those of simple modules in that category. We also obtain a classification of projective-injective modules in the full BGG category $\\mathcal O$ for all simple classical Lie superalgebras. We then classify and give an explicit combinatorial description of parabolic subalgebras of the periplectic Lie superalgebras and apply our results to study their tilting modules in more detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-15T16:37:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "tilting modules",
      "periplectic lie superalgebras",
      "arbitrary classical lie superalgebra",
      "projective-injective modules",
      "parabolic bgg category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}