{
  "id": "1505.01047",
  "version": "v1",
  "published": "2015-05-05T15:44:58.000Z",
  "updated": "2015-05-05T15:44:58.000Z",
  "title": "Representations of affine superalgebras and mock theta functions III",
  "authors": [
    "Victor G. Kac",
    "Minoru Wakimoto"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study modular invariance of normalized supercharacters of tame integrable modules over an affine Lie superalgebra, associated to an arbitrary basic Lie superalgebra $ \\mathfrak{g}. $ For this we develop a several step modification process of multivariable mock theta functions, where at each step a Zwegers' type \"modifier\" is used. We show that the span of the resulting modified normalized supercharacters is $ SL_2(\\mathbb{Z}) $-invariant, with the transformation matrix equal, in the case the Killing form on $\\mathfrak{g}$ is non-degenerate, to that for the subalgebra $ \\mathfrak{g}^! $ of $ \\mathfrak{g}, $ orthogonal to a maximal isotropic set of roots of $ \\mathfrak{g}. $",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-05T15:44:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine superalgebras",
      "arbitrary basic lie superalgebra",
      "representations",
      "affine lie superalgebra",
      "study modular invariance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150501047K"
    }
  }
}