{
  "id": "1508.03802",
  "version": "v1",
  "published": "2015-08-16T08:44:58.000Z",
  "updated": "2015-08-16T08:44:58.000Z",
  "title": "Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A",
  "authors": [
    "Monica Vazirani"
  ],
  "comment": "29 pages; to appear in Proc. Sympos. Pure Math. as part of the Proceedings of the 2012-2014 Southeastern Lie Theory Workshops",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We use Khovanov-Lauda-Rouquier algebras to categorify a crystal isomorphism between a highest weight crystal and the tensor product of a perfect crystal and another highest weight crystal, all in level 1 type A affine. The nodes of the perfect crystal correspond to a family of trivial modules and the nodes of the highest weight crystal correspond to simple modules, which we may also parameterize by $\\ell$-restricted partitions. In the case $\\ell$ is a prime, one can reinterpret all the results for the symmetric group in characteristic $\\ell$. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-16T08:44:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C08"
    ],
    "keywords": [
      "tensor product",
      "highest weight crystal correspond",
      "crystal operators correspond",
      "perfect crystal correspond",
      "categorify"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803802V"
    }
  }
}