Characters of equivariant D-modules on Veronese cones

摘要: For d > 1, we consider the Veronese map of degree on a complex vector space W , Ver_d : -> Sym^d w w^d and denote its image by Z. We describe characters simple GL(W)-equivariant holonomic D-modules supported In case when is 2, obtain counterexample to conjecture Levasseur exhibiting D-module Capelli type representation Sym^2 which contains no SL(W)-invariant sections. also study local cohomology modules H_Z^j(S), where S ring polynomial functions W. recover result Ogus showing that there only one module non-zero (namely in j = codim(Z)), moreover prove it determine character.