Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

摘要

We define the Virasoro algebra action on imaginary Verma modules for affine ${mathfrak{sl}(2)}$ and construct an analogue of the Knizhnik–Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.