Virasoro action on imaginary Verma modules and the operator form of the KZ-equation (Q1928842)

The authors construct an action of the Virasoro algebra on imaginary Verma modules for affine \(\mathfrak{sl}_2\). Further, the authors construct intertwining operators from an imaginary Verma module to the tensor product of an imaginary Verma module with a finite dimensional module and obtain an analogue of the operator form of the Knizhnik-Zamolodchikov equations. Both results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators, called imaginary Wakimoto modules.