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.
CITATION STYLE
Futorny, V., Morales, O., & Křižka, L. (2023). Admissible representations of simple affine vertex algebras. Journal of Algebra, 628, 22–70. https://doi.org/10.1016/j.jalgebra.2023.03.010
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