41 citations · 548 across the 118 of their papers we have counts for
138 papers
Categorical Lie-Rinehart modules and Shen-Larsson functors
Han Dai, Vyacheslav Futorny, Huimin Gao
We develop a categorical framework for Lie-Rinehart monoids and their weak modules in a symmetric monoidal category. Using crossed homomorphisms, we construct a natural action of t…
Representations of twisted quantum affine algebras
Juan Camilo Arias, Vyacheslav Futorny, Kailash C. Misra
We develop the representation theory of imaginary Verma modules for twisted quantum affine algebras and construct the corresponding Kashiwara algebras. The twisted case presents su…
Irreducibility of the tensor product of Yangian \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \) evaluation modules
Vyacheslav Futorny, Zheng Li, Jian Zhang
The evaluation homomorphism from the super Yangian \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \) to \( \mathrm{U}(\mathfrak{gl}_{m|n}) \) induces a \( \mathrm{Y}(\mathfrak{gl}_{m|n}) \)-mo…
Graded identities of the first Weyl algebra and its generalizations
V. Futorny, P. Koshlukov, J. Schwarz
We study the graded polynomial identities of the first Weyl algebra over an infinite field. The algebra satisfies no ordinary polynomial identities in characteristic 0.…
Whittaker constructions for quantum affine algebras
Vyacheslav Futorny, Santanu Tantubay
The goals of the paper are 3-fold. First, we revisit the construction of imaginary Whittaker modules over untwisted affine Kac-Moody Lie algebras. These modules are obtained using…
Representations of Super Yangians with Gelfand-Tsetlin bases
Vyacheslav Futorny, Zheng Li, Jian Zhang
The evaluation homomorphism from the super Yangian to the universal enveloping algebra allows one to regard the $\…