{
  "id": "1604.01622",
  "version": "v1",
  "published": "2016-04-06T13:42:50.000Z",
  "updated": "2016-04-06T13:42:50.000Z",
  "title": "Irreducible modules for equivariant map superalgebras and their extensions",
  "authors": [
    "Tiago Macedo",
    "Lucas Calixto"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\\mathfrak{g}$. The corresponding equivariant map superalgebra $M(\\mathfrak{g}, X)^\\Gamma$ is the Lie superalgebra of equivariant regular maps from $X$ to $\\mathfrak{g}$. In this paper we complete the classification of finite-dimensional irreducible $M(\\mathfrak{g}, X)^\\Gamma$-modules when $\\mathfrak{g}$ is a finite-dimensional simple Lie superalgebra, $X$ is of finite type, and $\\Gamma$ is a finite abelian group acting freely on the rational points of $X$. We also describe extensions between these irreducible modules in terms of extensions between modules for certain finite-dimensional Lie superalgebras. As an application, when $\\Gamma$ is trivial and $\\mathfrak{g}$ is of type $B(0,n)$, we describe the block decomposition of the category of finite-dimensional $M(\\mathfrak{g}, X)^\\Gamma$-modules in terms of spectral characters for $\\mathfrak{g}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-06T13:42:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B55",
      "17B56",
      "17B65"
    ],
    "keywords": [
      "irreducible modules",
      "extensions",
      "finite-dimensional simple lie superalgebra",
      "abelian group acting",
      "finite-dimensional lie superalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160401622M"
    }
  }
}