{
  "id": "1612.05815",
  "version": "v1",
  "published": "2016-12-17T19:51:21.000Z",
  "updated": "2016-12-17T19:51:21.000Z",
  "title": "The Duflo-Serganova functor and Grothendieck rings of Lie superalgebras",
  "authors": [
    "Crystal Hoyt",
    "Shifra Reif"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that the Duflo-Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a natural quotient of the Grothendieck ring, which is isomorphic to the ring of characters. We realize this homomorphism as a certain evaluation of functions related to the supersymmetry property. We use this realization to describe the kernel and image of the homomorphism induced by the Duflo-Serganova functor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-17T19:51:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "duflo-serganova functor",
      "grothendieck ring",
      "finite-dimensional contragredient lie superalgebra induces",
      "homomorphism",
      "finite-dimensional modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}