相关论文: Representations of Yangians associated with skew Y…

We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to…

Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including the quantized algebra of functions on GL(N) and the Yangian for gl(N). We prove a version of this theorem for the…

Let $GL_M$ be general linear Lie group over the complex field. The irreducible rational representations of the group $GL_M$ are labeled by pairs of partitions $\mu$ and $\tilde\mu$ such that the total number of non-zero parts of $\mu$ and…

We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion…

We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra $gl(1|1)$.

We study analogues of the Yangian of the Lie algebra $gl_N$ for the other classical Lie algebras $so_N$ and $sp_N$. We call them twisted Yangians. They are coideal subalgebras in the Yangian $Y(gl_N)$ of $gl_N$ and admit homomorphisms onto…

The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the…

We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their…

Let $G_M$ be one of the complex Lie groups $O_M$ and $Sp_M$. The irreducible finite-dimensional representations of the group $G_M$ are labeled by partitions $\mu$ satisfying certain extra conditions. Let $U$ be the representation of $G_M$…

We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra $\frak{osp}_{1|2}$. The representations are parameterized by monic polynomials in one…

Let $Y_{1|1}$ be the Yangian associated to the general linear Lie superalgebra $\mathfrak{gl}_{1|1}$, defined over an algebraically closed field $\mathbbm{k}$ of characteristic $p>2$. In this paper, we classify the finite dimensional…

Remarkable subalgebras of the Yangian for gl_n called the shifted Yangians were introduced in a recent work by Brundan and Kleshchev in relation to their study of finite W-algebras. In particular, in that work a classification of…

We study in detail the structure of the Yangian Y(gl(N)) and of some new Yangian-type algebras called twisted Yangians. The algebra Y(gl(N)) is a `quantum' deformation of the universal enveloping algebra U(gl(N)[x]), where gl(N)[x] is the…

Yangian-like algebras, associated with current R-matrices, different from the Yang ones, are introduced. These algebras are of two types. The so-called braided Yangians are close to the Reflection Equation algebras, arising from involutive…

The connection between simple Lie algebras and their Yangian algebras has a long history. In this work, we construct finite-dimensional representations of Yangian algebras $\mathsf{Y}(\mathfrak{sl}_{n})$ using the quiver approach. Starting…

We study highest weight representations of shifted Yangians over an algebraically closed field of characteristic 0. In particular, we classify the finite dimensional irreducible representations and explain how to compute their…

We classify the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{1|2n}$ in terms of the Drinfeld polynomials. The arguments rely on the description of the…

Let $Y_2$ be the Yangian associated to the general linear Lie algebra $\mathfrak{gl}_2$, defined over an algebraically closed field $\mathbbm{k}$ of characteristic $p > 0$. In this paper, we study the representation theory of the restricted…

We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…