{
  "id": "1112.3792",
  "version": "v1",
  "published": "2011-12-16T12:44:55.000Z",
  "updated": "2011-12-16T12:44:55.000Z",
  "title": "A New Functor from $D_5$-Mod to $E_6$-Mod",
  "authors": [
    "Xiaoping Xu"
  ],
  "comment": "45pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We find a new representation of the simple Lie algebra of type $E_6$ on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen's idea of mixed product, we construct a functor from $D_5$-{\\bf Mod} to $E_6$-{\\bf Mod}. A condition for the functor to map a finite-dimensional irreducible $D_5$-module to an infinite-dimensional irreducible $E_6$-module is obtained. Our general frame also gives a direct polynomial extension from irreducible $D_5$-modules to irreducible $E_6$-modules. The obtained infinite-dimensional irreducible $E_6$-modules are $({\\cal G},K)$-modules in terms of Lie group representations. The results could be used in studying the quantum field theory with $E_6$ symmetry and symmetry of partial differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-16T12:44:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B25",
      "22E46"
    ],
    "keywords": [
      "simple lie algebra",
      "lie group representations",
      "direct polynomial extension",
      "partial differential equations",
      "quantum field theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.3792X"
    }
  }
}