{
  "id": "2302.14477",
  "version": "v1",
  "published": "2023-02-28T10:36:04.000Z",
  "updated": "2023-02-28T10:36:04.000Z",
  "title": "Representation type of cyclotomic quiver Hecke algebras of type $A_\\ell^{(1)}$",
  "authors": [
    "Susumu Ariki",
    "Linliang Song",
    "Qi Wang"
  ],
  "comment": "62 pages, comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we completely determine the representation type of cyclotomic Khovanov-Lauda-Rouquier algebras of arbitrary level in affine type A, by using the quiver we construct. This result gives a complete classification for the representation type of blocks of cyclotomic Hecke algebras since cyclotomic KLR algebras of type $A^{(1)}_\\ell$ form a one-parameter family and cyclotomic Hecke algebras occur at a special parameter, i.e., $t=-2$ if $\\ell=1$ and $t=(-1)^{\\ell+1}$ if $\\ell\\geq2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-28T10:36:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "16G60",
      "17B65",
      "16G20"
    ],
    "keywords": [
      "cyclotomic quiver hecke algebras",
      "representation type",
      "dominant maximal weights",
      "cyclotomic hecke algebras occur",
      "affine type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}