{
  "id": "1107.3356",
  "version": "v2",
  "published": "2011-07-18T05:29:53.000Z",
  "updated": "2012-04-08T10:21:41.000Z",
  "title": "Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra",
  "authors": [
    "Andrey E. Mironov"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this paper we study self-adjoint commuting ordinary differential operators. We find sufficient conditions when an operator of fourth order commuting with an operator of order $4g+2$ is self-adjoint. We introduce an equation on coefficients of the self-adjoint operator of order four and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of arbitrary genus. These operators have polynomial coefficients and define commutative subalgebras of the first Weyl algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-08T10:21:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-adjoint commuting differential operators",
      "weyl algebra",
      "commutative subalgebras",
      "study self-adjoint commuting ordinary differential",
      "self-adjoint commuting ordinary differential operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.3356M"
    }
  }
}