{
  "id": "1209.3477",
  "version": "v2",
  "published": "2012-09-16T11:48:37.000Z",
  "updated": "2013-09-28T10:57:06.000Z",
  "title": "The space $L^2$ on semi-infinite Grassmannian over finite field",
  "authors": [
    "Yury A. Neretin"
  ],
  "comment": "32pp",
  "journal": "Advances in Mathematics Volume 250, 15, 2014, Pages 320-350",
  "doi": "10.1016/j.aim.2013.09.014",
  "categories": [
    "math.RT",
    "math.CA",
    "math.PR"
  ],
  "abstract": "We construct a $GL$-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space $L^2$ over the Grassmannian on irreducible representations. The spectrum is discrete, spherical functions on the Grassmannian are given in terms of the Al Salam--Carlitz orthogonal polynomials. We also construct an invariant measure on the corresponding space of flags.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-28T10:57:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E65",
      "20G40",
      "60B05",
      "37L40",
      "33D45",
      "43A05",
      "22B99"
    ],
    "keywords": [
      "finite field",
      "semi-infinite grassmannian",
      "invariant measure",
      "salam-carlitz orthogonal polynomials",
      "natural group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3477N"
    }
  }
}