{
  "id": "1801.09316",
  "version": "v1",
  "published": "2018-01-28T23:39:54.000Z",
  "updated": "2018-01-28T23:39:54.000Z",
  "title": "Gelfand-Tsetlin Theory for Rational Galois Algebras",
  "authors": [
    "Vyacheslav Futorny",
    "Dimitar Grantcharov",
    "Luis Enrique Ramírez",
    "Pablo Zadunaisky"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and prove a simplicity criterion for these modules. The results hold for modules defined over standard Galois orders of type $A$ - a large class of rings that include the universal enveloping algebra of $\\mathfrak{gl} (n)$ and the finite $W$-algebras of type $A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-28T23:39:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G99",
      "17B10"
    ],
    "keywords": [
      "rational galois algebras",
      "gelfand-tsetlin theory",
      "study gelfand-tsetlin modules",
      "bgg differential operators",
      "standard galois orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}