Geometrical Aspects of Representation Theory

1. Geometry of primitive ideals. 1.1. Let G be a complex algebraic group with Lie algebra g. I would like to have a geometric picture for the structure of primitive ideals of the enveloping algebra U(g). The only universal answer known so far is the "orbit method," saying that primitive ideals should correspond to coadjoint orbits in the dual g* of g. Sometimes this principle doesn't work, however. The situation may be improved if one looks not just onto an orbit itself but on a certain "resolution data" over it as well. I propose to consider diagrams like this: