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arXiv · 2112.14631

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

Boris Feigin·Michio Jimbo·Evgeny Mukhin
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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.

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Boris Feigin, Michio Jimbo, Evgeny Mukhin. 2021-12-29. Quantum Toroidal Comodule Algebra of Type $A_{n-1}$ and Integrals of Motion. https://doi.org/10.3842/sigma.2022.051

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