Annihilating ideals and tilting functors

Abstract

We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra. For the sake of completeness, the classification of annihilating ideals is borrowed from our previous work, q-alg/9711011; the part on tilting functors is new.