Radial components, prehomogeneous vector spaces, and rational Cherednik algebras
| dc.creator | Levasseur, Thierry | |
| dc.date | 2008-01-08 | |
| dc.date | 2008-01-31 | |
| dc.date.accessioned | 2026-07-07T08:57:14Z | |
| dc.date.available | 2026-07-07T08:57:14Z | |
| dc.description | 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. | |
| dc.description | 33 pages. Minor corrections | |
| dc.identifier | https://arxiv.org/abs/0801.1289 | |
| dc.identifier | http://arxiv.org/abs/0801.1289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146888 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S32; 14L30; 17B45 | |
| dc.title | Radial components, prehomogeneous vector spaces, and rational Cherednik algebras | |
| dc.type | text |