# Colloquium abstracts

Philbert Nang
ENS, Gabon
April 18, 2013

D-modules on a class of G-representations:  We give an answer to abstract Capelli problem: Let (G, V) be a multiplicity free finite dimensional representation of a connected reductive complex Lie group G and G' be its derived subgroup. Assume that the categorical quotient V//G is one dimensional, i.e., there exists a polynomial f generating the algebra of G'-invariant polynomials on V (\C[V]^G' = \C[f]) and such that f \not\in \C[V]^G ). We prove that the category of regular holonomic D_V-modules invariant under the action of G is equivalent to the category of graded modules of finite type over a suitable algebra.