{
  "id": "1207.2274",
  "version": "v6",
  "published": "2012-07-10T09:29:16.000Z",
  "updated": "2017-02-20T20:12:41.000Z",
  "title": "Critical points of master functions and integrable hierarchies",
  "authors": [
    "Alexander Varchenko",
    "Daniel Wright"
  ],
  "comment": "Latex 42 pages, misprints corrected",
  "categories": [
    "math.AG",
    "math.CO",
    "nlin.SI"
  ],
  "abstract": "We consider the population of critical points generated from the trivial critical point of the master function with no variables and associated with the trivial representation of the affine Lie algebra $\\hat{\\frak{sl}}_N$. We show that the critical points of this population define rational solutions of the equations of the mKdV hierarchy associated with $\\hat{\\frak{sl}}_N$. We also construct critical points from suitable $N$-tuples of tau-functions. The construction is based on a Wronskian identity for tau-functions. In particular, we construct critical points from suitable $N$-tuples of Schur polynomials and prove a Wronskian identity for Schur polynomials.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-05-24T02:32:26.000Z",
      "comment": "AmsLaTeX, 42 pages, misprints corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v6",
      "updated": "2017-02-20T20:12:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "master function",
      "integrable hierarchies",
      "construct critical points",
      "schur polynomials",
      "wronskian identity"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2274V"
    }
  }
}