{
  "id": "1912.06427",
  "version": "v1",
  "published": "2019-12-13T11:46:07.000Z",
  "updated": "2019-12-13T11:46:07.000Z",
  "title": "On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$",
  "authors": [
    "Abel Lacabanne"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We propose a conjecture relating two different sets of characters for the complex reflection group $G(d,1,n)$. From one side, the characters are afforded by Calogero-Moser cells, a conjectural generalisation of Kazhdan-Lusztig cells for a complex reflection group. From the other side, the characters arise from a level $d$ irreducible integrable representations of $\\mathcal{U}_q(\\mathfrak{sl}_{\\infty})$. We prove this conjecture in some cases: in full generality for $G(d,1,2)$ and for generic parameters for $G(d,1,n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-13T11:46:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex reflection group",
      "cellular characters",
      "conjecture",
      "generic parameters",
      "full generality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}