{
  "id": "math/0604336",
  "version": "v2",
  "published": "2006-04-14T13:00:07.000Z",
  "updated": "2006-12-22T16:28:06.000Z",
  "title": "Kostant modules in blocks of category ${\\mathcal O}_S$",
  "authors": [
    "Brian D. Boe",
    "Markus Hunziker"
  ],
  "comment": "25 pages, 2 tables, 6 figures, uses PSTricks; v.2: added Secs. 4 (BGG resolutions) and 7.5 (Minimal free resolutions), expanded Introduction",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper the authors investigate infinite-dimensional representations $L$ in blocks of the relative (parabolic) category ${\\mathcal O}_S$ for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in $L$ ``looks like'' the cohomology with coefficients in a finite-dimensional module, as in Kostant's theorem. A complete classification of these ``Kostant modules'' in regular blocks for maximal parabolics in the simply laced types is given. A complete classification is also given in arbitrary (singular) blocks for Hermitian symmetric categories.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-22T16:28:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "kostant modules",
      "complex simple lie algebra",
      "complete classification",
      "hermitian symmetric categories",
      "maximal parabolics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4336B"
    }
  }
}