Admissible representations of simple affine vertex algebras

Vyacheslav Futorny; Oscar Armando Hernández Morales; Libor Křižka

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arXiv · 2107.11128

Admissible representations of simple affine vertex algebras

Vyacheslav Futorny·Oscar Armando Hernández Morales·Libor Křižka

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Abstract

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. 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.

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BibTeX RIS

Vyacheslav Futorny, Oscar Armando Hernández Morales, Libor Křižka. 2021-07-23. Admissible representations of simple affine vertex algebras. https://arxiv.org/abs/2107.11128

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