{
  "id": "1301.0120",
  "version": "v3",
  "published": "2013-01-01T19:04:49.000Z",
  "updated": "2015-04-04T15:34:37.000Z",
  "title": "On representations of rational Cherednik algebras in complex rank",
  "authors": [
    "Inna Entova Aizenbud"
  ],
  "comment": "Exposition improved in latest version, typos fixed",
  "journal": "Represent. Theory 18 (2014), 361-407",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study a family of abelian categories O_{c, t} depending on complex parameters c, t which are interpolations of the O-category for the rational Cherednik algebra H_c(t) of type A, where t is a positive integer. We define the notion of a Verma object in such a category (a natural analogue of the notion of Verma module). We give some necessary conditions and some sufficient conditions for the existence of a non-trivial morphism between two such Verma objects. We also compute the character of the irreducible quotient of a Verma object for sufficiently generic values of parameters c, t, and prove that a Verma object of infinite length exists in O_{c, t} only if c is rational and c < 0. We also show that for every rational c < 0 there exists a rational t < 0 such that there exists a Verma object of infinite length in O_{c, t}. The latter result is an example of a degeneration phenomenon which can occur in rational values of t, as was conjectured by P. Etingof.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-27T17:31:44.000Z",
      "comment": "39 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-04T15:34:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "18D10"
    ],
    "keywords": [
      "rational cherednik algebra",
      "verma object",
      "complex rank",
      "infinite length",
      "representations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Represent. Theory"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0120E"
    }
  }
}