Verma-type modules for quantum affine Lie algebras

Let g be an untwisted affine Kac-Moody algebra and M(J) (lambda) a Verma-type module for g with J-highest weight lambda is an element of P. We construct quantum Verma-type modules M(J)(q) (lambda) over the quantum group U(q)(g), investigate their properties and show that M(J)(q) (lambda) is a true quantum deformation of M(J)(lambda) in the sense that the weight structure is preserved under the deformation. We also analyze the submodule structure of quantum Verma-type modules.