Admissible representations of simple affine vertex algebras.

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra L κ (sl n + 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 sl 2 -induced modules in these orbits. In particular, simple admissible sl 2 -induced modules are fully classified for the principal nilpotent orbit. [ABSTRACT FROM AUTHOR]