On the classification of primitive ideals for complex classical Lie algebras, I

Abstract

This paper is the fourth and last in the series “On the classification of primitive ideals for complex classical Lie algebras, extending the main results of [5] to type D. Here the generalized τ-invariant defined in [5] must be defined in a different way, as there is no pair of adjacent simple roots in type D with different lengths. Instead we attach a family of operators to a quadruple of simple roots spanning a subsystem of type D4, each of them taking either one or two values, like the corresponding operators in types B and C, and use these to characterize primitive ideals via their generalized τ-invariants.