Quantum Toroidal Comodule Algebra of Type 𝐴ₙ₋₁ and Integrals of Motion

Abstract

We introduce an algebra 𝒦ₙ which has the structure of a left comodule over the quantum toroidal algebra of type 𝐴ₙ₋₁. Algebra 𝒦ₙ is a higher rank generalization of 𝒦₁, which provides a uniform description of deformed 𝑊 algebras associated with Lie (super)algebras of types BCD. We show that 𝒦ₙ possesses a family of commutative subalgebras.