{
  "id": "math/9812148",
  "version": "v1",
  "published": "1998-12-28T01:45:29.000Z",
  "updated": "1998-12-28T01:45:29.000Z",
  "title": "Fixed point formula and loop group actions",
  "authors": [
    "Sheldon X. Chang"
  ],
  "comment": "77 pages, 7 figures, uses newcommand.sty, in AMS-LaTex",
  "categories": [
    "math.AG",
    "math.SG"
  ],
  "abstract": "The main goal of this paper is to obtain a formula for the T-equivariant Riemann-Roch number of certain G-spaces which are the finite dimensional models of certain infinite dimensional spaces with Hamiltonian LG-actions, here T is a maximal torus of the semi-simple Lie group G. Unlike its finite dimensional cousin, the formula obtained here only needs to valuate on a finite subgroup of T depending on the 'level' of the LG-action and the dual Coxeter number of G, due to a fundamental cancelation. If the fixed-point sets of elements of the finite subgroup do not intersect the compactification locus used in constructing the finite dimensional model, the fixed point formula has a particularly simple form, which will be shown for the case of Verlinde formula. This paper was written in early 1997 and had limited circulation, before I left academia. The version here has a computer time-stamp 6/10/97. I have been urged by former colleaques to archive this article together with its sequels on the net.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-28T01:45:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed point formula",
      "loop group actions",
      "finite dimensional model",
      "finite subgroup",
      "finite dimensional cousin"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12148C"
    }
  }
}