{
  "id": "1507.06298",
  "version": "v1",
  "published": "2015-07-22T19:55:51.000Z",
  "updated": "2015-07-22T19:55:51.000Z",
  "title": "A general approach to Heisenberg categorification via wreath product algebras",
  "authors": [
    "Daniele Rosso",
    "Alistair Savage"
  ],
  "comment": "46 pages",
  "categories": [
    "math.RT",
    "math.QA",
    "math.RA"
  ],
  "abstract": "We associate a monoidal category $\\mathcal{H}_B$, defined in terms of planar diagrams, to any graded Frobenius superalgebra $B$. This category acts naturally on modules over the wreath product algebras associated to $B$. To $B$ we also associate a (quantum) lattice Heisenberg algebra $\\mathfrak{h}_B$. We show that, provided $B$ is not concentrated in degree zero, the Grothendieck group of $\\mathcal{H}_B$ is isomorphic, as an algebra, to $\\mathfrak{h}_B$. For specific choices of Frobenius algebra $B$, we recover existing results, including those of Khovanov and Cautis--Licata. We also prove that certain morphism spaces in the category $\\mathcal{H}_B$ contain generalizations of the degenerate affine Hecke algebra. Specializing $B$, this proves an open conjecture of Cautis--Licata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-22T19:55:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D10",
      "17B10",
      "17B65",
      "19A22"
    ],
    "keywords": [
      "wreath product algebras",
      "heisenberg categorification",
      "general approach",
      "degenerate affine hecke algebra",
      "lattice heisenberg algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150706298R"
    }
  }
}