Primitive ideals and representations
Let \({\mathfrak g}\) be a semisimple Lie algebra over \({\mathbb{C}}\) and M a \({\mathfrak g}\)-module. Fix a primitive ideal I in the enveloping algebra U(\({\mathfrak J})\). The author studies the consequences in \({\mathfrak n}\)- cohomology of M of the condition \(IM=0\). Using a derived functor construction an analogue of the Casselman-Osborn theorem is proved in category \({\mathcal O}\) where the whole primitive ideal is fixed.
scientific article; zbMATH DE number 3964120