8 citations · 20 across the 10 of their papers we have counts for
12 papers
Double Yangian, Factorization, and qKZ-equation for Cotangent Lie Algebras
Raschid Abedin, Wenjun Niu
In this paper, we construct the dual and double of the Yangian associated with a cotangent Lie algebra $\m…
Hecke modifications of conformal blocks outside the critical level
Raschid Abedin, Giovanni Felder, Robert Windesheim
We define Hecke modifications of conformal blocks over affine Lie algebras at non-critical level by using the Hecke modifications of the underlying -bundles. We show that this p…
Quantum groupoids from moduli spaces of -bundles
Raschid Abedin, Wenjun Niu
In a previous work, we have constructed the Yangian of the cotangent Lie algebra for a simple Lie algebra , fr…
Generalized classical Yang-Baxter equation and regular decompositions
Raschid Abedin, Stepan Maximov, Alexander Stolin
The focus of the paper is on constructing new solutions of the generalized classical Yang-Baxter equation (GCYBE) that are not skew-symmetric. Using regular decompositions of finit…
Yangian for cotangent Lie algebras and spectral -matrices
Raschid Abedin, Wenjun Niu
In this paper, we present a canonical quantization of Lie bialgebra structures on the formal power series with coefficients in the cotangent Lie algebra $\m…
The -matrix structure of Hitchin systems via loop group uniformization
Raschid Abedin
In this work, the description of the moduli space of principal -bundles as double quotient of loop groups is used to construct an étale local -matrix for the Hitchin integrab…
Classification of -bialgebra structures on power series algebras
Raschid Abedin
In this paper, we use algebro-geometric methods in order to derive classification results for so-called -bialgebra structures on the power series algebra for certai…
Topological Manin pairs and -type series
Raschid Abedin, Stepan Maximov, Alexander Stolin
Lie subalgebras of , complementary to the diagonal embedding of and Lagrangian…
Topological Lie bialgebra structures and their classification over
Raschid Abedin, Stepan Maximov, Alexander Stolin +1
This paper is devoted to a classification of topological Lie bialgebra structures on the Lie algebra , where is a finite-dimensional simple…
Geometrization of solutions of the generalized classical Yang-Baxter equation and a new proof of the Belavin-Drinfeld trichotomy
Raschid Abedin
We study solutions to a generalized version of the classical Yang-Baxter equation (CYBE) with values in a central simple Lie algebra over a field of characteristic 0 from an algebr…
Classification of classical twists of the standard Lie bialgebra structure on a loop algebra
Raschid Abedin, Stepan Maximov
The standard Lie bialgebra structure on an affine Kac-Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. In this paper we…
Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
Raschid Abedin, Igor Burban
This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang-Baxter equation. We regard trigonometric s…