{
  "id": "1409.5207",
  "version": "v1",
  "published": "2014-09-18T07:04:55.000Z",
  "updated": "2014-09-18T07:04:55.000Z",
  "title": "Whittaker modules for the derivation Lie algebra of torus with two variables",
  "authors": [
    "Haifeng Lian",
    "Xiufu Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathcal{L}$ be the derivation Lie algebra of ${\\mathbb C}[t_1^{\\pm 1},t_2^{\\pm 1}]$. Given a triangle decomposition $\\mathcal{L} =\\mathcal{L}^{+}\\oplus\\mathfrak{h}\\oplus\\mathcal{L}^{-}$, we define a nonsingular Lie algebra homomorphism $\\psi:\\mathcal{L}^{+}\\rightarrow\\mathbb{C}$ and the universal Whittaker $\\mathcal{L}$-module $W_{\\psi}$ of type $\\psi$. We obtain all Whittaker vectors and submodules of $W_{\\psi}$, and all simple Whittaker $\\mathcal{L}$-modules of type $\\psi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-18T07:04:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derivation lie algebra",
      "whittaker modules",
      "nonsingular lie algebra homomorphism",
      "universal whittaker",
      "whittaker vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5207L"
    }
  }
}