{
  "id": "2412.09397",
  "version": "v1",
  "published": "2024-12-12T16:03:06.000Z",
  "updated": "2024-12-12T16:03:06.000Z",
  "title": "On the basic representation of the double affine Hecke algebra at critical level",
  "authors": [
    "J. F. van Diejen",
    "E. Emsiz",
    "I. N. Zurrián"
  ],
  "comment": "7 pages",
  "journal": "Journal of Algebra and Its Applications, Vol. 23, No. 03, 2450061 (2024)",
  "doi": "10.1142/S0219498824500610",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct the basic representation of the double affine Hecke algebra at critical level $q=1$ associated to an irreducible reduced affine root system $R$ with a reduced gradient root system. For $R$ of untwisted type such a representation was studied by Oblomkov [O04] and further detailed by Gehles [G06] in the presence of minuscule weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-12T16:03:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "17B22",
      "17B67",
      "33D80"
    ],
    "keywords": [
      "double affine hecke algebra",
      "basic representation",
      "critical level",
      "reduced affine root system",
      "reduced gradient root system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}