{
  "id": "math/0409371",
  "version": "v1",
  "published": "2004-09-20T23:13:53.000Z",
  "updated": "2004-09-20T23:13:53.000Z",
  "title": "On the structure and characters of weight modules",
  "authors": [
    "Dimitar Grantcharov"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak g$ be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra {\\bf W}$(n)$. We study weight $\\mathfrak g$-modules using a method inspired by Mathieu's classification of the simple weight modules with finite weight multiplicities over reductive Lie algebras, \\cite{M}. Our approach is based on the fact that every simple weight $\\mathfrak g$-module with finite weight multiplicities is obtained via a composition of a twist and localization from a highest weight module. This allows us to transfer many results for category ${\\cal O}$ modules to the category of weight modules with finite weight multiplicities. As a main application of the method we reduce the problems of finding a ${\\mathfrak g}_0$-composition series and a character formula for all simple weight modules to the same problems for simple highest weight modules. In this way, using results of Serganova we obtain a character formula for all simple weight {\\bf W}$(n)$-modules and all simple atypical nonsingular ${\\mathfrak s}{\\mathfrak l} (m|1)$-modules. Some of our results are new already in the case of a classical reductive Lie algebra $\\mathfrak g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-20T23:13:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "finite weight multiplicities",
      "simple weight modules",
      "reductive lie algebra",
      "simple highest weight modules",
      "character formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9371G"
    }
  }
}