Kostant cascades and centrally generated primitive ideals of U(n)

Let g be a classical finite-dimensional complex Lie algebra, and n be the nilradical of a Borel subalgebra b of g. The Dixmier map provides a homeomorphism between the space of primitive ideals of the enveloping algebra U(n) and the space of coadjoint orbits on the dual space n*. Our goal is to describe centrally generated primitive ideals of U(n). The center of U(n) can be described using the Kostant cascade of the root system of g, and the description of the centrally generated primitive ideals is given in related terms of so-called Kostant forms.

We also provide a similar description of the center and the centrally generated primitive ideals of U(n) for a simple infinite-dimensional finitary classical Lie algebra g and some special choice of n. The talk is based on our joint work with Ivan Penkov.