{
  "id": "1607.04034",
  "version": "v1",
  "published": "2016-07-14T08:49:04.000Z",
  "updated": "2016-07-14T08:49:04.000Z",
  "title": "On the category of finite-dimensional representations of $\\OSPrn$: Part I",
  "authors": [
    "Michael Ehrig",
    "Catharina Stroppel"
  ],
  "journal": "Representation theory - current trends and perspectives, EMS Series of Congress Reports, European Mathematical Society (EMS), 2016",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the combinatorics of the category F of finite-dimensional modules for the orthosymplectic Lie supergroup OSP(r|2n). In particular we present a positive counting formula for the dimension of the space of homomorphism between two projective modules. This refines earlier results of Gruson and Serganova. Moreover, for each block B of F we construct an algebra A(B) whose module category shares the combinatorics with B. It arises as a subquotient of a suitable limit of type D Khovanov algebras. It will turn out that A(B) is isomorphic to the endomorphism algebra of a minimal projective generator of B. This provides a direct link from F to parabolic categories O of type B or D, with maximal parabolic of type A, to the geometry of isotropic Grassmannians of types B/D and to Springer fibres of types C/D. We also indicate why F is not highest weight in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-14T08:49:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "16S37",
      "16D50",
      "17B20"
    ],
    "keywords": [
      "finite-dimensional representations",
      "module category shares",
      "orthosymplectic lie supergroup",
      "refines earlier results",
      "minimal projective generator"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}