{
  "id": "math/0406282",
  "version": "v4",
  "published": "2004-06-14T21:27:17.000Z",
  "updated": "2005-10-19T22:57:10.000Z",
  "title": "Algebraic groups over a 2-dimensional local field: some further constructions",
  "authors": [
    "Dennis Gaitsgory",
    "David Kazhdan"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this kind are not on vector spaces, but rather on pro-vector spaces. In this paper we present some further constructions related to this theory. The main results include: 1) General theorems insuring representability of covariant functors, 2) Study of the functor of semi-invariants, which is an analog of the functor of semi-infinite cohomology for infinite-dimensional Lie algebras, 3) Construction of representations from the moduli space of $G$-bundles on algebraic curve over $K$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-10-19T22:57:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local field",
      "algebraic group",
      "construction",
      "infinite-dimensional lie algebras",
      "general theorems insuring representability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6282G"
    }
  }
}