Centrally generated primitive ideals of \(U(\mathfrak{n})\) for exceptional types

Let \(\mathfrak{g}\) be a complex semisimple Lie algebra, \(\mathfrak{b}\) be a Borel subalgebra of \(\mathfrak{g}\), \(\mathfrak{n}\) be the nilradical of \(\mathfrak{b}\), and \(U(\mathfrak{n})\) be the universal enveloping algebra of \(\mathfrak{n}\). We study primitive ideals of \(U(\mathfrak{n})\). Almost all primitive ideals are centrally generated, i.e., are generated by their intersections with the center \(Z(\mathfrak{n})\) of \(U(\mathfrak{n})\). We present an explicit characterization of the centrally generated primitive ideals of \(U(\mathfrak{n})\) in terms of the Dixmier map and the Kostant cascade in the case when \(\mathfrak{g}\) 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 \(U(\mathfrak{n})\) for an arbitrary semisimple algebra \(\mathfrak{g}\).