2008/01/08 by Thierry Levasseur, Levasseur, Thierry · 1 citation
Mathematics · #14L30 #16S32 #17B45 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:14L30 #msc:16S32 #msc:17B45
paper · pdf · doi:10.48550/arxiv.0801.1289
33 pages. Minor corrections
openalex publication_date 2008/01/08 · arxiv created 2008/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.