Quantum Toroidal Comodule Algebra of Type $A_{n-1}$ and Integrals of Motion

Abstract

We introduce an algebra ${\mathcal{K}}_n$ which has a structure of a left comodule over the quantum toroidal algebra of type $A_{n-1}$. Algebra ${\mathcal{K}}_n$ is a higher rank generalization of ${\mathcal{K}}_1$, which provides a uniform description of deformed $W$ algebras associated with Lie (super)algebras of types BCD. We show that ${\mathcal{K}}_n$ possesses a family of commutative subalgebras.

References in corpus (3)

• Toroidal q-Opers
• The $R$-matrix of the quantum toroidal algebra $U_{q,t}({\stackrel{..}{\mathrm{gl}}}_1)$ in the Fock module
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra