Verma-type Modules for Quantum Affine Lie Algebras

الأصل · EN

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