{
  "id": "1809.03622",
  "version": "v1",
  "published": "2018-09-10T22:52:29.000Z",
  "updated": "2018-09-10T22:52:29.000Z",
  "title": "A Kazhdan-Lusztig algorithm for Whittaker modules",
  "authors": [
    "Anna Romanov"
  ],
  "comment": "50 pages; preliminary version, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study a category of Whittaker modules over a complex semisimple Lie algebra by realizing it as a category of twisted D-modules on the associated flag variety using Beilinson-Bernstein localization. The main result of this paper is the development of a geometric algorithm for computing the composition multiplicities of standard Whittaker modules. This algorithm establishes that these multiplicities are determined by a collection of polynomials we refer to as Whittaker Kazhdan-Lusztig polynomials. In the case of trivial nilpotent character, this algorithm specializes to the usual algorithm for computing multiplicities of composition factors of Verma modules using Kazhdan-Lusztig polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T22:52:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47",
      "14F10"
    ],
    "keywords": [
      "kazhdan-lusztig algorithm",
      "complex semisimple lie algebra",
      "trivial nilpotent character",
      "whittaker kazhdan-lusztig polynomials",
      "standard whittaker modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}