Primitive ideals of U(sl(infty))

We describe explicitly the primitive ideals in U(sl(infty)).We show that all such ideals are the annihilators of integrable
simple sl(infty)-modules. The only maximal ideal in U(sl(infty) is the augmentation ideal. We also prove a Duflo-type theorem describing primitive ideals as annihilators of highest-weight modules. Not all Borel subalgebras realize primitive ideals in this way:
the ones that do, are ideal Borel subalgebras. This is joint work with Alexey Petukhov.