An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras
An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras
Abstract We discover a large class of simple affine vertex algebras $V_{k} ({\mathfrak{g}})$, associated to basic Lie superalgebras ${\mathfrak{g}}$ at non-admissible collapsing levels $k$, having exactly one irreducible ${\mathfrak{g}}$-locally finite module in the category ${\mathcal O}$. In the case when ${\mathfrak{g}}$ is a Lie algebra, we prove a complete reducibility …