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Deformations of $\mathcal W$ algebras via quantum toroidal algebras by Feigin, B.; Jimbo, M.; Mukhin, E.; Vilkoviskiy, I. is a scholarly article available to read on EtoBox.

What is Deformations of $\mathcal W$ algebras via quantum toroidal algebras about?

The deformed $\mathcal W$ algebras of type $\textsf{A}$ have a uniform description in terms of the quantum toroidal $\mathfrak{gl}_1$ algebra $\mathcal E$. We introduce a comodule algebra $\mathcal K$ over $\mathcal E$ which gives a uniform construction of basic deformed $\mathcal W$ currents and screening operators in types $\textsf{B},\textsf{C},\textsf{D}$ including twisted and supersymmetric cases. We show that a completion of algebra $\mathcal K$ contains three commutative subalgebras. In particular, it allows us to obtain a commutative family of integrals of motion associated with affine Dynkin diagrams of all non-exceptional types except $\textsf{D}^{(2)}_{\ell+1}$. We also obtain in a uniform way deformed finite and affine Cartan matrices in all classical types together with a number of new examples, and discuss the corresponding screening operators.

Author

Feigin, B.; Jimbo, M.; Mukhin, E.; Vilkoviskiy, I.

Published

2020

Language

EN