Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks

Symmetry Integrability and Geometry-Methods and Applications

article

Mikhail Bershtein¹  Roman Gonin² 

[1] Landau Institute for Theoretical Physics;Center for Advanced Studies, Skolkovo Institute of Science and Technology

关键词: quantum algebras;    toroidal algebras;    W-algebras;    conformal blocks;    Nekrasov partition function;    Whittaker vector;   

DOI  :  10.3842/SIGMA.2020.077

来源: National Academy of Science of Ukraine

【 摘 要 】

We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally identified with the basic level 1 representation of affine $\mathfrak{gl}_n$. We also study twisted $W$-algebras of $\mathfrak{sl}_n$ acting on these Fock modules. As an application, we prove the relation on $q$-deformed conformal blocks which was conjectured in the study of $q$-deformation of isomonodromy/CFT correspondence.

【 授权许可】

Unknown