Starting with a four-dimensional gauge theory approach to rational, elliptic, and
trigonometric solutions of the Yang-Baxter equation, we determine the corresponding …

Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras,
which are q-deformations of the classical W. We also define their free field realizations, ie …

Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a
simple comultiplication for the quantum current operators. In this Letter, we will present a …

Bethe vectors are found for quantum integrable models associated with the supersymmetric
Yangians $ Y (\mathfrak {gl}(m| n) $ in terms of the current generators of the Yangian double …

We introduce the shifted quantum affine algebras. They map homomorphically into the
quantized K-theoretic Coulomb branches of 3 d N= 4 3 d {\mathcal N= 4 SUSY quiver gauge …

Abstract Given an affine Kac–Moody algebra, we explain how to construct a coproduct on its
associated Yangian. In order to prove that this coproduct is an algebra homomorphism, we …

This review is meant to be an account of the properties of the infinite-dimensional quantum
group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral …

In this paper, we prove that the quantum toroidal algebra U q, q‾(gl¨ n) is isomorphic to the
double shuffle algebra of Feigin and Odesskii for the cyclic quiver. The shuffle algebra …

A bstract In these notes we study integrable structure of conformal field theory by means of
Liouville reflection operator/Maulik Okounkov R-matrix. We discuss relation between RLL …

Studying the algebraic structure of the double DY (g) of the Yangian Y (g), we present the
triangular decomposition of DY (g) and a factorization for the canonical pairing of the …