SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
Abstract
We study certain representations of quantum toroidal gl1 algebra for q = t. We construct explicit bosonization of the Fock modules Fu(n′,n) with a nontrivial slope n′ /n. As a vector space, it is naturally identified with the basic level 1 representation of affine gln . We also study twisted W-algebras of sln 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.
