Virasoro action on Imaginary Verma modules and the operator form of the   KZ-equation
  We define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules. 
Ben Cox, Vyacheslav Futorny, Renato Martins
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