Centrally generated primitive ideals of [formula omitted] for exceptional types

Abstract

Let g be a complex semisimple Lie algebra, let b be a Borel subalgebra of g, let n be the nilradical of b, and let U(n) be the universal enveloping algebra of n. We study primitive ideals of U(n). Almost all primitive ideals are centrally generated, i.e., are generated by their intersections with the center Z(n) of U(n). We present an explicit characterization of the centrally generated primitive ideals of U(n) in terms of the Dixmier map and the Kostant cascade in the case when g is a simple algebra of exceptional type. (For classical simple Lie algebras, a similar characterization was obtained by Ivan Penkov and the first author.) As a corollary, we establish a classification of centrally generated primitive ideals of U(n) for an arbitrary semisimple algebra g.