{
  "id": "math/0505370",
  "version": "v1",
  "published": "2005-05-18T03:03:09.000Z",
  "updated": "2005-05-18T03:03:09.000Z",
  "title": "On the Ext groups between Weyl modules for GL_n",
  "authors": [
    "Upendra Kulkarni"
  ],
  "comment": "plain TeX, 37 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "This paper studies extension groups between certain Weyl modules for the algebraic group GL_n over the integers. Main results include: (1) A complete determination of Ext groups between Weyl modules whose highest weights differ by a single root and (2) Determination of Ext^1 between an exterior power of the defining representation and any Weyl module. The significance of these results for modular representation theory of GL_n is discussed in several Remarks. Notably the first result leads to a calculation of Ext groups between neighboring Weyl modules for GL_n and also recovers the GL_n case of a recent result of Andersen. Some generalities about Ext groups between Weyl modules and a brief overview of known results about these groups are also included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-18T03:03:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G10"
    ],
    "keywords": [
      "ext groups",
      "paper studies extension groups",
      "modular representation theory",
      "highest weights differ",
      "first result"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5370K"
    }
  }
}