{
  "id": "1903.02626",
  "version": "v1",
  "published": "2019-03-06T21:55:14.000Z",
  "updated": "2019-03-06T21:55:14.000Z",
  "title": "Gauge modules for the Lie algebras of vector fields on affine varieties",
  "authors": [
    "Yuly Billig",
    "Jonathan Nilsson",
    "André Zaidan"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\\mathcal{V}$ of vector fields on the variety. We prove that a gauge module corresponding to a simple $\\mathfrak{gl}_N$-module is irreducible as a module over the Lie algebra of vector fields unless it appears in the de Rham complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-06T21:55:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "lie algebra",
      "vector fields",
      "affine varieties",
      "smooth irreducible affine algebraic variety",
      "gauge modules admitting compatible actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}