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

Mikhail Bershtein, Roman Gonin

We study certain representations of quantum toroidal ${\mathfrak{gl}}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules ${\mathcal{F}}_u^{(n^{\prime },n)}$ with a non…