{
  "id": "1402.0727",
  "version": "v1",
  "published": "2014-02-04T13:30:18.000Z",
  "updated": "2014-02-04T13:30:18.000Z",
  "title": "Representations of affine superalgebras and mock theta functions II",
  "authors": [
    "Victor G. Kac",
    "Minoru Wakimoto"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that the normalized supercharacters of principal admissible modules, associated to each integrable atypical module over the affine Lie superalgebra $\\widehat{sl}_{2|1}$ can be modified, using Zwegers' real analytic corrections, to form an $SL_2(\\mathbf{Z})$-invariant family of functions. Using a variation of Zwegers' correction, we obtain a similar result for $\\widehat{osp}_{3|2}$. Applying the quantum Hamiltonian reduction, this leads to new families of positive energy modules over the $N=2$ (resp. $N=3$) superconformal algebras with central charge $c=3 (1-\\frac{2m+2}{M})$, where $m \\in \\mathbf{Z}_{\\geq 0}, M \\in \\mathbf{Z}_{\\geq 2}$, gcd$(2m+2,M)=1$ if $m>0$ (resp. $c=-3\\frac{2m+1}{M}$, where $m \\in \\mathbf{Z}_{\\geq 0}, M \\in \\mathbf{Z}_{\\geq 2}$ gcd$(4m +2, M) =1)$, whose modified supercharacters form an $SL_2(\\mathbf{Z})$-invariant family of functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-04T13:30:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mock theta functions",
      "affine superalgebras",
      "representations",
      "affine lie superalgebra",
      "real analytic corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1280127,
      "adsabs": "2014arXiv1402.0727K"
    }
  }
}