Verma-type Modules for Quantum Affine Lie Algebras

Details Verma-type Modules for Quantum Affine Lie Algebras Verma-type Modules for Quantum Affine Lie Algebras

2000-10-31

arxiv.org/abs/math/0010322v1

Mathematics

Quantum Algebra

24 pages, AMSTeX 2.0

Scientific paper

Let g be an untwisted affine Kac-Moody algebra and M_J(lambda) a Verma-type module for g with J-highest integral weight lambda. 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(\l) 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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