14 citations · 26 across the 8 of their papers we have counts for
12 papers
Simple -modules that are torsion free -modules of rank
Dimitar Grantcharov, Libor Krizka, Volodymyr Mazorchuk
We provide an explicit classification of all simple -modules that are torsion free of rank over the Cartan subalgebra. We also establish a similar result for t…
Generalized Grothendieck's simultaneous resolution and associated varieties of simple affine vertex algebras
Tomoyuki Arakawa, Vyacheslav Futorny, Libor Krizka
The closure of a Diximier sheet is the image of a generalized Grothendieck's simultaneous resolution. We show that the associated variety of simple affine vertex algebras is contai…
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…
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…
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…
Generalized Verma modules over U_q(sl_n(C))
Vyacheslav Futorny, Libor Krizka, Jian Zhang
We construct realizations of quantum generalized Verma modules for U_q(sl_n(C)) by quan- tum differential operators. Taking the classical limit q ! 1 provides a realization of clas…