5 papers
Kostant theorem for special filtered algebras
Vyacheslav Futorny, Serge Ovsienko
A famous result of Kostant states that the universal enveloping algebra of a semisimple complex Lie algebra is a free module over its center. We prove an analogue of this result fo…
Harish-Chandra modules for Yangians
Vyacheslav Futorny, Alexander Molev, Serge Ovsienko
We study Harish-Chandra representations of Yangian for gl(2). We prove an analogue of Kostant theorem showing that resterited Yangians for gl(2) are free modules over certain maxim…
Weyl algebra modules
Viktor Bekkert, Georgia Benkart, Vyacheslav Futorny
We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weig…
Derived categories of Schur algebras
Viktor Bekkert, Vyacheslav Futorny
We classify the derived tame Schur and infinitesimal Schur algebras and describe indecomposable objects in their derived categories.
Verma-type Modules for Quantum Affine Lie Algebras
Vyacheslav M. Futorny, Duncan J. Melville, Alexander N. Grishkov
Let g be an untwisted affine Kac-Moody algebra and M_J(lambda) a Verma-type module for g with J-highest integral weight lambda. We construct quantum Verma-type modules M_J^q(lambda…