{
  "id": "1610.03194",
  "version": "v1",
  "published": "2016-10-11T05:23:11.000Z",
  "updated": "2016-10-11T05:23:11.000Z",
  "title": "Toda systems and hypergeometric equations",
  "authors": [
    "Chang-Shou Lin",
    "Zhaohu Nie",
    "Juncheng Wei"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP",
    "math.AG",
    "math.DG",
    "nlin.SI"
  ],
  "abstract": "This paper establishes certain existence and classification results for solutions to $SU(n)$ Toda systems with three singular sources at 0, 1, and $\\infty$. First, we determine the necessary conditions for such an $SU(n)$ Toda system to be related to an $n$th order hypergeometric equation. Then, we construct solutions for $SU(n)$ Toda systems that satisfy the necessary conditions and also the interlacing conditions from Beukers and Heckman. Finally, for $SU(3)$ Toda systems satisfying the necessary conditions, we classify, under a natural reality assumption, that all the solutions are related to hypergeometric equations. This proof uses the Pohozaev identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T05:23:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47",
      "33C20"
    ],
    "keywords": [
      "necessary conditions",
      "th order hypergeometric equation",
      "natural reality assumption",
      "paper establishes",
      "singular sources"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}