A characteristic variety for the primitive spectrum of a semisimple lie algebra

Abstract

M. Duflo [5] has recently shown that the primitive spectrum of a split semisimple Lie algebra over a field of characteristic zero is just the set of annihilators of simple quotients of Verma modules. Following this a characteristic variety is defined for two-sided ideals in the enveloping algebra and used to give a new and elementary proof of Duflo's ordering principle on the fibre of primitive ideals with the same central character. The main new result of this paper (Theorem 15) exhibits a decomposition of the Weyl group into disjoint subsets (cells) so that each point in a given cell defines the same ideal (via Duflo's theorem). It is conjectured that different cells correspond to different ideals, a result which would classify the primitive spectrum.

Work supported by the C.N.R.S.