According to Drinfeld, a quantum group is the same as a Hopf algebra. This includes as
special cases, the algebra of regular functions on an algebraic group and the envelo** …

algebras and deformations of W-algebras Page 174 http://dx. doi. org/10.1090/conm/248/03823
Contemporary Mathematics Volume 248, 1999 The q-characters of representations of quantum …

We lift the lattice of translations in the extended affine Weyl group to a braid group action on
the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop …

We study finite-dimensional representations of quantum affine algebras using q-characters.
We prove the conjectures from [FR] and derive some of their corollaries. In particular, we …

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 …

Generalized Baxter's relations on the transfer matrices (also known as Baxter's TQ relations)
are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we …

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 …

We collect and systematize general definitions and facts on the application of quantum
groups to the construction of functional relations in the theory of integrable systems. As an …

In this paper we study general quantum affinizations U_q(g) of symmetrizable quantum Kac-
Moody algebras and we develop their representation theory. We prove a triangular …

A bstract We analyze\(\mathcal {N}= 1\) theories on S 5 and S 4× S 1, showing how their
partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We …