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math.RT2021
Admissible representations of simple affine vertex algebras
Vyacheslav Futorny, Oscar Armando Hernández Morales, Libor Křižka
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 admi…
math.RT2020
Positive energy representations of affine vertex algebras
Vyacheslav Futorny, Libor Křižka
We construct new families of positive energy representations of affine vertex algebras together with their free field realizations by using localization technique. We introduce the…
math.RT2019★ 1 cited
Twisting functors and Gelfand--Tsetlin modules over semisimple Lie algebras
Vyacheslav Futorny, Libor Krizka
We associate to an arbitrary positive root of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor of the category of $\mfrak{g}$-module…