Towards trigonometric deformation of ${\widehat{\mathfrak{sl}}}_2$ coset VOA

Abstract

We discuss the quantization of the ${\widehat{\mathfrak{sl}}}_2$ coset vertex operator algebra $\mathcal{W}D(2,1;\alpha )$ using the bosonization technique. We show that after quantization there exist three families of commuting integrals of motion coming from three copies of the quantum toroidal algebra associated to ${\mathfrak{gl}}_2$.

Latex, 20 pages

References in corpus (2)

• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• The $({\mathfrak{gl}}_m,{\mathfrak{gl}}_n$) duality in the quantum toroidal setting

Cited by in corpus (3)

• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• A Note on Quiver Quantum Toroidal Algebra
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$