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

Boris Feigin, National Research University Higher School of Economics, Russia, Michio Jimbo, Evgeny Mukhin, Rikkyo University, Japan, Indiana University Purdue University Indianapolis, USA
2022 Symmetry, Integrability and Geometry: Methods and Applications  
We introduce an algebra K n which has a structure of a left comodule over the quantum toroidal algebra of type A n−1 . Algebra K n is a higher rank generalization of K 1 , which provides a uniform description of deformed W algebras associated with Lie (super)algebras of types BCD. We show that K n possesses a family of commutative subalgebras.
doi:10.3842/sigma.2022.051 fatcat:d2hcgb22drgmrnk5q7km4stwgi