An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras

Abstract

© 2018 The Author(s). Published by Oxford University Press. All rights reserved. We discover a large class of simple affine vertex algebras Vk (g), associated to basic Lie superalgebras g at non-admissible collapsing levels k, having exactly one irreducible g-locally finite module in the category O. In the case when g is a Lie algebra, we prove a complete reducibility result for Vk(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra Vk (g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V-1/2 (Cn) and V-4(E7), we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.