{
  "id": "1410.6917",
  "version": "v1",
  "published": "2014-10-25T12:37:44.000Z",
  "updated": "2014-10-25T12:37:44.000Z",
  "title": "A new involution for quantum loop algebras",
  "authors": [
    "Jyun-Ao Lin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "In this article, we introduce a completion $\\widehat{U}^+_v(\\mathcal{L}\\mathfrak{g})$ of the positive half of the quantum affinization $U^+_v(\\mathcal{L}\\mathfrak{g})$ of a symmetrizable Kac-Moody algebra $\\mathfrak{g}$. On $\\widehat{U}^+_v(\\mathcal{L}(\\mathfrak{g}))$, we define a new \"bar-involution\" and construct the analogue Kashiwara's operators. We conjecture that the resulting pair $(\\widehat{\\mathcal{L}},\\widehat{\\mathcal{B}})$ is a crystal basis which provides the existence of the \"canonical basis\" on the (completion of the) of the positive half of the quamtum affinization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-25T12:37:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum loop algebras",
      "involution",
      "positive half",
      "analogue kashiwaras operators",
      "quantum affinization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6917L"
    }
  }
}