{
  "id": "math/0109033",
  "version": "v2",
  "published": "2001-09-05T10:46:22.000Z",
  "updated": "2002-04-01T01:37:36.000Z",
  "title": "Gamma sheaves on reductive groups",
  "authors": [
    "Alexander Braverman",
    "David Kazhdan"
  ],
  "comment": "to appear in Schur memorial volume",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "The purpose of this paper is to introduce and study certain irreducible perverse l-adic sheaves on a reductive group G over a finite field (we call them gamma-sheaves). One can construct such a sheaf starting with (almost) every finite-dimensional representation of the Langlands dual group. We present conjecture connecting the above sheaves with generalized gamma-functions introduced in our previous paper. We also conjecture that the convolution functor with the above sheaves enjoys certain nice properties (in particular, we compute the convolution of a gamma-sheaf with a character sheaf). We prove the above conjectures for G of semi-simple rank 0 or 1 and (partially) for G=GL(n).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-04-01T01:37:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive group",
      "gamma sheaves",
      "irreducible perverse l-adic sheaves",
      "conjecture",
      "langlands dual group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9033B"
    }
  }
}