{
  "id": "1401.0845",
  "version": "v2",
  "published": "2014-01-04T21:34:17.000Z",
  "updated": "2015-07-29T18:17:26.000Z",
  "title": "Fully commutative elements of type D and homogeneous representations of KLR-algebras",
  "authors": [
    "Gabriel Feinberg",
    "Kyu-Hwan Lee"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type $D_n$, and study the combinatorics of these subsets, revealing hidden structures. (We do not consider type $A_n$ first, since a similar decomposition for type $A_n$ is trivial.) As an application, we classify and enumerate the homogeneous representations of the Khovanov-Lauda-Rouquier algebras of type $D_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-04T21:34:17.000Z",
      "title": "Homogeneous representations of KLR-algebras and fully commutative elements",
      "abstract": "The Khovanov-Lauda-Rouquier (KLR) algebra arose out of attempts to categorify quantum groups. Kleshchev and Ram proved a result reducing the representation theory of these algebras to the study of irreducible cuspidal representations. In finite types, these cuspidal representations are part of a larger class of homogeneous representations, which are related to fully commutative elements of Coxeter groups. In this paper, we decompose the set of fully commutative elements into natural subsets, when the Coxeter group is of type $A_n$ or $D_n$, and study combinatorics of these subsets, revealing hidden structures. Thereby we classify and enumerate the homogeneous representations for KLR algebras of types $A_n$ and $D_n$.",
      "comment": "24 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-29T18:17:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully commutative elements",
      "homogeneous representations",
      "klr-algebras",
      "coxeter group",
      "cuspidal representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0845F"
    }
  }
}