{
  "id": "1504.03924",
  "version": "v1",
  "published": "2015-04-15T14:27:35.000Z",
  "updated": "2015-04-15T14:27:35.000Z",
  "title": "Koszul gradings on Brauer algebras",
  "authors": [
    "Michael Ehrig",
    "Catharina Stroppel"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We show that the Brauer algebra over the complex numbers for an integral parameter delta can be equipped with a grading, in the case of delta being non-zero turning it into a graded quasi-hereditary algebra. In which case it is Morita equivalent to a Koszul algebra. This is done by realizing the Brauer algebra as an idempotent truncation of a certain level two VW-algebra for some large positive integral parameter N. The parameter delta appears then in the choice of a cyclotomic quotient. This cyclotomic VW-algebra arises naturally as an endomorphism algebra of a certain projective module in parabolic category O for an even special orthogonal Lie algebra. In particular, the graded decomposition numbers are given by the associated parabolic Kazhdan-Lusztig polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-15T14:27:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16W20",
      "16W50",
      "17B20",
      "17B45"
    ],
    "keywords": [
      "brauer algebra",
      "koszul gradings",
      "special orthogonal lie algebra",
      "integral parameter delta",
      "associated parabolic kazhdan-lusztig polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403924E"
    }
  }
}