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arXiv · 1906.00600

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

Mikhail Bershtein·Roman Gonin
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Abstract

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.

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BibTeXRIS

Mikhail Bershtein, Roman Gonin. 2019-06-03. Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks. https://doi.org/10.3842/sigma.2020.077

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