{
  "id": "math/0508162",
  "version": "v3",
  "published": "2005-08-09T06:51:20.000Z",
  "updated": "2006-03-02T23:01:34.000Z",
  "title": "Bases for certain cohomology representations of the symmetric group",
  "authors": [
    "Anthony Henderson"
  ],
  "comment": "30 pages; in third version, more references are added, making further connections with general theory of cohomology of local systems on hyperplane complements; also the consequences of the main result for cohomology dimensions and module generators are stated more explicitly",
  "journal": "J. Algebraic Combin. 24 (2006), no. 4, pp. 361-390.",
  "doi": "10.1007/s10801-006-0018-3",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around the coordinate hyperplanes and trivial monodromy around all other hyperplanes. In the case where the local system is equivariant for the symmetric group, we write the cohomology groups as direct sums of inductions of one-dimensional characters of subgroups. This relies on an equivariant description of the Orlik-Solomon algebras of full monomial reflection groups (wreath products of the symmetric group with a cyclic group). The combinatorial models involved are certain representations of these wreath products which possess bases indexed by labelled trees.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-03-02T23:01:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C30",
      "58A10"
    ],
    "keywords": [
      "symmetric group",
      "cohomology representations",
      "cohomology groups",
      "full monomial reflection groups",
      "wreath products"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8162H"
    }
  }
}