{
  "id": "0909.5487",
  "version": "v1",
  "published": "2009-09-30T03:13:48.000Z",
  "updated": "2009-09-30T03:13:48.000Z",
  "title": "Integral homology of loop groups via Langlands dual groups",
  "authors": [
    "Zhiwei Yun",
    "Xinwen Zhu"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "Let K be a connected compact Lie group, and G be its complexification. The homology of the based loop group \\Omega K with integer coefficients is naturally a \\ZZ-Hopf algebra. After possibly inverting 2 or 3, we identify H_*(\\Omega K,\\ZZ) with the Hopf algebra of algebraic functions on B^\\vee_e, where B^\\vee is a Borel subgroup of the Langlands dual group scheme G^\\vee of G and B^\\vee_e is the centralizer in B^\\vee of a regular nilpotent element e\\in\\Lie B^\\vee. We also give a similar interpretation for the equivariant homology of \\Omega K under the maximal torus action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-30T03:13:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57T10",
      "20G07"
    ],
    "keywords": [
      "loop group",
      "integral homology",
      "langlands dual group scheme",
      "connected compact lie group",
      "regular nilpotent element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.5487Y"
    }
  }
}