Related papers: Double Yangians and quantum vertex algebras, I

For any simply-laced GCM $A$, a $\mathbb C[[\hbar]]$-algebra $\widehat{\mathcal{DY}}(A)$ was introduced in [KL1], where it was proved that the universal vacuum $\widehat{\mathcal{DY}}(A)$-module ${\mathcal{V}}_A(\ell)$ for any fixed level…

This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian…

We give a new realization of $Y(sl_3)$ via Cartan-Weyl elements. An algebraic description of Yangian Double $DY(sl_3)$, explicit comultiplication formulas and universal R-matrix are obtained in these terms.

Yangian Double $DY(A(m,n))$ of Lie Superalgebra $A(m,n)$ is described in terms of generators and defining relations. It is proved triangular decomposition for Yangian $Y(A(m,n))$ and its quantum double $DY(A(m,n))$ as a corollary of PBW…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained…

In this paper, we construct the dual $Y^*_\hbar(\mathfrak d)$ and double $DY_\hbar (\mathfrak d)$ of the Yangian $Y_\hbar (\mathfrak d)$ associated with a cotangent Lie algebra $\mathfrak d=T^*\mathfrak g$. We define a coherent…

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of $\hbar$-adic nonlocal vertex algebra and $\hbar$-adic…

We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent…

We consider the Etingof-Kazhdan quantum vertex algebra $\mathcal{V}^c(R)$ associated with the trigonometric and elliptic $R$-matrix of type $A.$ We establish a connection between (restricted) modules for the $h$-Yangian…

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras…

The existence of dual structures in a Yangian Y(g) signify that the latter belongs to multidimensional naturally parametrized variety of Hopf algebras. These varieties have boundaries containing Yangians Y(a) inequivalent to the original…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field $\mathbf{k}$, and let $\widehat{\Lambda}$ be the repetitive algebra of $\Lambda$. In this article, we prove that if $\widehat{V}$ is a left…

In this note, we consider the twisted Yangians $\text{Y}(\mathfrak{g}_N)$ associated with the orthogonal and symplectic Lie algebras $\mathfrak{g}_N=\mathfrak{o}_N,\mathfrak{sp}_N$. First, we introduce a certain subalgebra…

Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…

We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are…

A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangians structures of dynamical type are in…

In the previous paper, we constructed a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the standard degreewise completion of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$. In this…

Starting from a given S-matrix of an integrable quantum field theory in $1+1$ dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by…

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras…

We construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(q_u-q_{u+1})$ to the universal enveloping algebra of a $W$-algebra associated with $\mathfrak{gl}(\sum_{s=1}^lq_s)$ and a nilpotent element of type…