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17 papers
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…
Drinfeld Realization for Quantum Affine Orthosymplectic Superalgebras
Luan Bezerra, Vyacheslav Futorny, Iryna Kashuba
A well-defined braid groupoid action is an essential tool for constructing the new Drinfeld realization of a quantum affine superalgebra. For quantum affine orthosymplectic superal…
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…
Whittaker Modules for W type Cartan Lie superalgebras
Vyacheslav Futorny, Santanu Tantubay
We consider the category of Whittaker modules for the Lie superalgebra of vector fields on . For any we show the equivale…
Representations of Super Yangians with Gelfand-Tsetlin bases
Vyacheslav Futorny, Zheng Li, Jian Zhang
The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\…