{
  "id": "1412.5098",
  "version": "v1",
  "published": "2014-12-16T17:50:03.000Z",
  "updated": "2014-12-16T17:50:03.000Z",
  "title": "Equivariant Map Queer Lie Superalgebras",
  "authors": [
    "Lucas Calixto",
    "Adriano Moura",
    "Alistair Savage"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra $\\mathfrak{q}$ that are equivariant with respect to the action of a finite group $\\Gamma$ acting on $X$ and $\\mathfrak{q}$. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that $\\Gamma$ is abelian and acts freely on $X$. We show that such representations are parameterized by a certain set of $\\Gamma$-equivariant finitely supported maps from $X$ to the set of isomorphism classes of irreducible finite-dimensional representations of $\\mathfrak{q}$. In the special case where $X$ is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-16T17:50:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B10"
    ],
    "keywords": [
      "equivariant map queer lie superalgebra",
      "irreducible finite-dimensional representations",
      "twisted loop queer superalgebra",
      "isomorphism classes",
      "equivariant finitely supported maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5098C"
    }
  }
}