Related papers: Yangian characters and classical W-algebras
We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…
We produce explicit generators of the classical W-algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie algebra of type $G_2$. The generators are given by determinant…
The Kirillov--Reshetikhin modules W^{r,s} are finite-dimensional representations of quantum affine algebras U'_q(g), labeled by a Dynkin node r of the affine Kac--Moody algebra g and a positive integer s. In this paper we study the…
Starting from a finite-dimensional representation of the Yangian $Y(\mathfrak{g})$ for a simple Lie algebra $\mathfrak{g}$ in Drinfeld's original presentation, we construct a Hopf algebra $X_\mathcal{I}(\mathfrak{g})$, called the extended…
Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the…
We construct a four-parameter family of affine Yangian algebras by gluing two copies of the affine Yangian of $\mathfrak{gl}_1$. Our construction allows for gluing operators with arbitrary (integer or half integer) conformal dimension and…
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…
We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain…
We express the classical r-matrix of AdS/CFT in terms of tensor products involving an infinite family of generators, which takes a form suggestive of the universal expression obtained from a Yangian double. This should provide an insight…
Associated to all quasi-split Satake diagrams of type ADE and even spherical coweights $\mu$, we introduce the shifted iYangians ${}^\imath Y_\mu$ and establish their PBW bases. We construct the iGKLO representations of ${}^\imath Y_\mu$,…
We consider the centers of the affine vertex algebras at the critical level associated with simple Lie algebras. We derive new formulas for generators of the centers in the classical types. We also give a new formula for the Capelli-type…
Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of characteristic 0) and its nilpotent element e.…
We introduce a new family of Poisson vertex algebras $\mathcal{W}(\mathfrak{a})$ analogous to the classical $\mathcal{W}$-algebras. The algebra $\mathcal{W}(\mathfrak{a})$ is associated with the centralizer $\mathfrak{a}$ of an arbitrary…
We address two problems regarding the structure and representation theory of finite W-algebras associated with the general linear Lie algebras. Finite W-algebras can be defined either via the Whittaker model of Kostant or, equivalently, by…
Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…
$W$-algebras are certain algebraic structures associated to a finite dimensional Lie algebra $\mathfrak g$ and a nilpotent element $f$ via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical…
We define a family of graded restricted modules for the polynomial current algebra associated to a simple Lie algebra. We study the graded character of these modules and show that they are the same as the graded characters of certain…
We give a new proof of the fact that the super Yangian of general linear Lie superalgebra is isomorphic to the finite W-superalgebra of the general linear Lie superalgebra associated to a rectangular nilpotent element.
Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…
The quantum super Yangian $Y_q(gl(M|N))$ associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is…