{
  "id": "0801.1289",
  "version": "v2",
  "published": "2008-01-08T17:37:56.000Z",
  "updated": "2008-01-31T17:37:28.000Z",
  "title": "Radial components, prehomogeneous vector spaces, and rational Cherednik algebras",
  "authors": [
    "Thierry Levasseur"
  ],
  "comment": "33 pages. Minor corrections",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let V be a finite dimensional representation of the connected complex reductive group H. Denote by G the derived subgroup of H and assume that the categorical quotient of V by G is one dimensional. In this situation there exists a homomorphism, denoted by rad, from the algebra A of G-invariant differential operators on V to the first Weyl algebra. We show that the image of rad is isomorphic to the spherical subalgebra of a Cherednik algebra, whose parameters are determined by the b-function of the relative invariant associated to the prehomogeneous vector space (H : V). If (H : V) is furthemore assumed to be multiplicity free we obtain a Howe duality between a set of representations of G and modules over a subalgebra of the associative Lie algebra A. Some applications to holonomic modules and H-equivariant D-modules on V are also given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-31T17:37:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S32",
      "14L30",
      "17B45"
    ],
    "keywords": [
      "prehomogeneous vector space",
      "rational cherednik algebras",
      "radial components",
      "g-invariant differential operators",
      "first weyl algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.1289L"
    }
  }
}