{
  "id": "1905.05620",
  "version": "v1",
  "published": "2019-05-14T14:02:00.000Z",
  "updated": "2019-05-14T14:02:00.000Z",
  "title": "Embedding Deligne's category $\\mathrm{Rep}(S_t)$ in the Heisenberg category",
  "authors": [
    "Samuel Nyobe Likeng",
    "Alistair Savage",
    "appendix with Christopher Ryba"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\\mathrm{Rep}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-14T14:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D10",
      "20C30",
      "17B10"
    ],
    "keywords": [
      "embedding delignes category",
      "heisenberg category",
      "faithful linear monoidal functor",
      "grothendieck rings",
      "symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}