{
  "id": "1605.07759",
  "version": "v1",
  "published": "2016-05-25T07:16:39.000Z",
  "updated": "2016-05-25T07:16:39.000Z",
  "title": "Classification of solutions to general Toda systems with singular sources",
  "authors": [
    "Chang-Shou Lin",
    "Zhaohu Nie",
    "Juncheng Wei"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math.DG",
    "math.RT",
    "nlin.SI"
  ],
  "abstract": "We classify all the solutions to the elliptic Toda system associated to a general simple Lie algebra with singular sources at the origin and with finite energy. The solution space is shown to be parametrized by a subgroup of the corresponding complex Lie group. We also show the quantization result for the finite integrals. This work generalizes the previous works in [Lin, Wei, Ye] and [Nie] for Toda systems of types $A$ and $B, C$. However, a more Lie-theoretic method is needed here for the general case, and the method relies heavily on the structure theories of the local solutions and of the $W$-invariants for the Toda system. This work will have applications to nonabelian Chern-Simons-Higgs gauge theory and to the mean field equations of Toda type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-25T07:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "35J91",
      "17B80"
    ],
    "keywords": [
      "general toda systems",
      "singular sources",
      "general simple lie algebra",
      "classification",
      "nonabelian chern-simons-higgs gauge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}