{
  "id": "1310.1596",
  "version": "v1",
  "published": "2013-10-06T16:31:24.000Z",
  "updated": "2013-10-06T16:31:24.000Z",
  "title": "On multiplication of double cosets for $\\GL(\\infty)$ over a finite field",
  "authors": [
    "Yury A. Neretin"
  ],
  "comment": "7pp",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We consider a group $GL(\\infty)$ and its parabolic subgroup $B$ corresponding to partition $\\infty=\\infty+m+\\infty$. Denote by $P$ the kernel of the natural homomorphism $B\\to GL(m)$. We show that the space of double cosets of $GL(\\infty)$ by $P$ admits a natural structure of a semigroup. In fact this semigroup acts in subspaces of $P$-fixed vectors of some unitary representations of $GL(\\infty)$ over finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-06T16:31:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40",
      "22E65",
      "22B99"
    ],
    "keywords": [
      "finite field",
      "double cosets",
      "multiplication",
      "unitary representations",
      "semigroup acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.1596N"
    }
  }
}