{
  "id": "1405.1691",
  "version": "v3",
  "published": "2014-05-07T18:32:12.000Z",
  "updated": "2015-12-22T11:55:54.000Z",
  "title": "Highest weight categories and strict polynomial functors",
  "authors": [
    "Henning Krause"
  ],
  "comment": "28 pages. This is a completely revised version (twice as long as version 2). The first part about highest weight categories over an arbitrary commutative base ring is new. Also the title has been changed",
  "categories": [
    "math.RT",
    "math.AC",
    "math.AT"
  ],
  "abstract": "Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is explained, using the theory of Schur and Weyl functors. A consequence is the well-known fact that Schur algebras are quasi-hereditary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-27T21:55:25.000Z",
      "title": "The highest weight structure for strict polynomial functors",
      "abstract": "We explain the highest weight structure for categories of strict polynomial functors, using the theory of Schur functors. A consequence is the well-known fact that Schur algebras are quasi-hereditary.",
      "comment": "14 pages. Version 2: added duality for weight spaces and historical references for the Cauchy decomposition",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-12-22T11:55:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strict polynomial functors",
      "highest weight structure",
      "schur functors",
      "well-known fact",
      "schur algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.1691K"
    }
  }
}