A geometric proof of Duflo's Theorem

Abstract

Let $R$ be a commutative ring: we explain the Beilinson-Bernstein localisation mechanism for sheaves of homogeneous twisted differential operators defined over a smooth, separated, locally of finite type $R$-scheme. As an application, we give a new proof of Duflo's theorem characterising the primitive ideals of the enveloping algebra of a complex semisimple Lie algebra.