{
  "id": "0707.0659",
  "version": "v1",
  "published": "2007-07-04T16:44:09.000Z",
  "updated": "2007-07-04T16:44:09.000Z",
  "title": "Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus",
  "authors": [
    "Yuly Billig",
    "Alexander Molev",
    "Ruibin Zhang"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the Lie algebra of vector fields. We prove this result by studying vertex algebras associated with the Lie algebra of vector fields on a torus and solving non-commutative differential equations that we derive using the vertex algebra technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-04T16:44:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B66",
      "17B69"
    ],
    "keywords": [
      "vector fields",
      "lie algebra",
      "simple modules",
      "vertex algebra technique",
      "generalized verma modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0659B"
    }
  }
}