Verma-type Modules for Quantum Affine Lie Algebras
Vyacheslav M. Futorny, Duncan J. Melville, Alexander N. Grishkov
Abstract
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.
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