{
  "id": "1508.06188",
  "version": "v1",
  "published": "2015-08-25T15:31:47.000Z",
  "updated": "2015-08-25T15:31:47.000Z",
  "title": "Classification of solutions to Toda systems of types $C$ and $B$ with singular sources",
  "authors": [
    "Zhaohu Nie"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "nlin.SI"
  ],
  "abstract": "In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type $A$ with singular sources is generalized to Toda systems of types $C$ and $B$. Like in the $A$ case, the solution space is shown to be parametrized by the abelian subgroup and a subgroup of the unipotent subgroup in the Iwasawa decomposition of the corresponding complex simple Lie group. The method is by studying the Toda systems of types $C$ and $B$ as reductions of Toda systems of type $A$ with symmetries. The theories of Toda systems as integrable systems as developed in [Leznov, Saveliev, Nie], in particular the $W$-symmetries and the iterated integral solutions, play essential roles in this work, together with certain characterizing properties of minors of symplectic and orthogonal matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-25T15:31:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "35J91",
      "17B80"
    ],
    "keywords": [
      "toda systems",
      "singular sources",
      "classification",
      "corresponding complex simple lie group",
      "play essential roles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150806188N"
    }
  }
}