{
  "id": "1612.08152",
  "version": "v1",
  "published": "2016-12-24T08:08:17.000Z",
  "updated": "2016-12-24T08:08:17.000Z",
  "title": "Whittaker coinvariants for $\\mathrm{GL}(m|n)$",
  "authors": [
    "Jonathan Brundan",
    "Simon M. Goodwin"
  ],
  "comment": "60 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $W_{m|n}$ be the (finite) $W$-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}(\\mathbb{C})$. In this paper we study the {\\em Whittaker coinvariants functor}, which is an exact functor from category $\\mathcal O$ for $\\mathfrak{gl}_{m|n}(\\mathbb{C})$ to a certain category of finite-dimensional modules over $W_{m|n}$. We show that this functor has properties similar to Soergel's functor $\\mathbb V$ in the setting of category $\\mathcal O$ for a semisimple Lie algebra. We also use it to compute the center of $W_{m|n}$ explicitly, and deduce some consequences for the classification of blocks of $\\mathcal O$ up to Morita/derived equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-24T08:08:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear lie superalgebra",
      "principal nilpotent orbit",
      "semisimple lie algebra",
      "whittaker coinvariants functor",
      "properties similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}