{
  "id": "1205.0870",
  "version": "v2",
  "published": "2012-05-04T07:07:58.000Z",
  "updated": "2012-07-09T15:49:18.000Z",
  "title": "Representations of affine Kac-Moody groups over local and global fields: a survey of some recent results",
  "authors": [
    "Alexander Braverman",
    "David Kazhdan"
  ],
  "comment": "To appear in the Proceedings of 6th European Congress of Mathematicians",
  "categories": [
    "math.RT",
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let G be a reductive algebraic group over a local field K or a global field F. It is well know that there exists a non-trivial and interesting representation theory of the group G(K) as well as the theory of automorphic forms on the corresponding adelic group. The purpose of this paper is to give a survey of some recent constructions and results, which show that there should exist an analog of the above theories in the case when G is replaced by the corresponding affine Kac-Moody group (which is essentially built from the formal loop group G((t)) of G). Specifically we discuss the following topics : affine (classical and geometric) Satake isomorphism, affine Iwahori-Hecke algebra, affine Eisenstein series and Tamagawa measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-09T15:49:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global field",
      "affine eisenstein series",
      "corresponding affine kac-moody group",
      "formal loop group",
      "affine iwahori-hecke algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0870B"
    }
  }
}