{
  "id": "1909.03499",
  "version": "v1",
  "published": "2019-09-08T16:29:55.000Z",
  "updated": "2019-09-08T16:29:55.000Z",
  "title": "The representation theory of seam algebras",
  "authors": [
    "Alexis Langlois-Rémillard",
    "Yvan Saint-Aubin"
  ],
  "comment": "29 pages, 3 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "The boundary seam algebras $\\mathsf{b}_{n,k}(\\beta=q+q^{-1})$ were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras $\\mathsf{b}_{n,k}(\\beta=q+q^{-1})$ is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Cramp\\'e and Poulain d'Andecy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-08T16:29:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation theory",
      "non-split short exact sequences",
      "boundary seam algebras",
      "two-dimensional statistical loop models",
      "poulain dandecy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}