{
  "id": "2006.01288",
  "version": "v1",
  "published": "2020-06-01T21:54:11.000Z",
  "updated": "2020-06-01T21:54:11.000Z",
  "title": "E-polynomials of character varieties for real curves",
  "authors": [
    "Thomas John Baird",
    "Michael Lennox Wong"
  ],
  "comment": "37 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.RT",
    "math.SG"
  ],
  "abstract": "We calculate the E-polynomial for a class of the (complex) character varieties $\\mathcal{M}_n^{\\tau}$ associated to a genus $g$ Riemann surface $\\Sigma$ equipped with an orientation reversing involution $\\tau$. Our formula (\\ref{GenFunctBig}) expresses the generating function $\\sum_{n=1}^{\\infty} E(\\mathcal{M}_n^{\\tau}) T^n$ as the plethystic logarithm of a product of sums indexed by Young diagrams. The proof uses point counting over finite fields, emulating \\cite{HRV}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-01T21:54:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D22"
    ],
    "keywords": [
      "character varieties",
      "real curves",
      "e-polynomial",
      "orientation reversing involution",
      "finite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}