{
  "id": "1012.2095",
  "version": "v3",
  "published": "2010-12-09T19:44:33.000Z",
  "updated": "2015-02-28T22:40:07.000Z",
  "title": "A Brylinski filtration for affine Kac-Moody algebras",
  "authors": [
    "William Slofstra"
  ],
  "comment": "Typos and reference corrected",
  "journal": "Advances in Math. 229 (2), 2012, 968-983",
  "categories": [
    "math.RT"
  ],
  "abstract": "Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac-Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac-Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra cohomology vanishing result. We also give an example to show that the Poincare series of the principal nilpotent filtration is not always equal to the q-analog of weight multiplicity. Finally, we give some partial results for indefinite Kac-Moody algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-10T22:58:53.000Z",
      "comment": "14 pages; minor edits in prep. for submission",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-28T22:40:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine kac-moody algebras",
      "principal nilpotent filtration",
      "brylinski filtration",
      "lie algebra cohomology vanishing result",
      "poincare series"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2095S"
    }
  }
}