{
  "id": "1910.07066",
  "version": "v1",
  "published": "2019-10-15T21:48:47.000Z",
  "updated": "2019-10-15T21:48:47.000Z",
  "title": "Bernstein-Gelfand-Gelfand resolutions and the constructible $t$-structure",
  "authors": [
    "Gurbir Dhillon"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider analogues of the Bernstein-Gelfand-Gelfand resolution in a highest weight category $\\mathscr{P}$. We prove the resulting category of complexes is a chain-level lift of the heart of the constructible $t$-structure on its bounded derived category $D^b(\\mathscr{P})$. In particular, an object admits a Bernstein-Gelfand-Gelfand resolution if and only if a certain $\\operatorname{Ext}$ vanishing with costandard objects holds. These results appear to be new even for Category $\\mathscr{O}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T21:48:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bernstein-gelfand-gelfand resolution",
      "highest weight category",
      "costandard objects holds",
      "constructible",
      "chain-level lift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}