Admissible representations of simple affine vertex algebras

Abstract

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra Lκ(sln+1) with n∈N of admissible level κ. For admissible simple highest weight modules corresponding to the principal, subregular and maximal parabolic nilpotent orbits we give a realization using the Gelfand–Tsetlin theory, which also allows us to obtain a realization of certain classes of simple admissible sl2-induced modules in these orbits. In particular, simple admissible sl2-induced modules are fully classified for the principal nilpotent orbit.