{
  "id": "1907.11988",
  "version": "v1",
  "published": "2019-07-27T22:55:00.000Z",
  "updated": "2019-07-27T22:55:00.000Z",
  "title": "Heisenberg and Kac-Moody categorification",
  "authors": [
    "Jonathan Brundan",
    "Alistair Savage",
    "Ben Webster"
  ],
  "comment": "52 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac-Moody 2-category (and vice versa). This gives a way to construct Kac-Moody actions in many representation-theoretic examples which is independent of Rouquier's original approach via `control by K_0.' As an application, we prove an isomorphism theorem for generalized cyclotomic quotients of these categories, extending the known isomorphism between cyclotomic quotients of type A affine Hecke algebras and quiver Hecke algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-27T22:55:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "18D10"
    ],
    "keywords": [
      "kac-moody categorification",
      "cyclotomic quotients",
      "rouquiers original approach",
      "affine hecke algebras",
      "heisenberg category satisfying suitable finiteness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}