{
  "id": "1105.4510",
  "version": "v2",
  "published": "2011-05-23T14:19:59.000Z",
  "updated": "2012-12-03T08:08:53.000Z",
  "title": "The space of generalized G_2-theta functions of level one",
  "authors": [
    "Chloé Grégoire"
  ],
  "comment": "This paper has been withdrawn by the author since superseded by 1211.7186",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G_2 be the exceptional Lie group of automorphisms of the complex Cayley algebra and C be a generic, smooth, connected, projective curve over $\\mathbb{C}$ of genus at least 2. For a complex Lie group G, let H^0(M(G),L^k) be the space of generalized G-theta functions over C of level k, where M(G) denotes the moduli stack of principal G-bundles over C and L the ample line bundle that generates the Picard group Pic(M(G)). Using the map obtained from extension of structure groups, we prove that the space H^0(M(G_2),L) of generalized G-2-theta functions over C of level one and the invariant space of H^0(M(SL_2), L) \\otimes H^0(M(SL_2), L^3) under the action of 2-torsion elements of the Jacobian JC[2] are isomorphic. We also prove explicit links between H^0(M(G_2),L) and the space of generalized SL_3-theta functions of level one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-03T08:08:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex lie group",
      "exceptional lie group",
      "picard group pic",
      "ample line bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4510G"
    }
  }
}