Quantum deformations of imaginary Verma modules

Abstract

We construct quantum deformations of imaginary Verma modules over ( A (1) 1 )and show that, for generic q, imaginary Verma modules over ( A (1) 1 )can be deformed to those over the quantum group ( A (1) 1 )in such a way that the dimensions of the weight spaces are invariant under the deformation. We also prove the PBW theorem for with respect to the triangular decomposition induced from the root partition corresponding to the imaginary Verma modules.