{
  "id": "2210.02269",
  "version": "v1",
  "published": "2022-10-05T13:53:50.000Z",
  "updated": "2022-10-05T13:53:50.000Z",
  "title": "Cohomology in singular blocks of parabolic category $\\mathcal{O}$",
  "authors": [
    "Jonathan Gruber"
  ],
  "comment": "14 pages. The main results were originally part of Section 5 of arXiv:2207.11999, from which they will subsequently be removed, citing this article instead",
  "categories": [
    "math.RT"
  ],
  "abstract": "We determine the dimensions of $\\mathrm{Ext}$-groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category $\\mathcal{O}$ for complex semisimple Lie algebras and affine Kac-Moody algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-05T13:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B55",
      "17B10",
      "17B67"
    ],
    "keywords": [
      "singular blocks",
      "parabolic category",
      "cohomology",
      "complex semisimple lie algebras",
      "dual generalized verma modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}