Verma-type Modules for Quantum Affine Lie Algebras

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 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...

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Veröffentlicht in:arXiv.org 2000-10
Hauptverfasser: Futorny, Vyacheslav M, Melville, Duncan J, Grishkov, Alexander N
Format: Artikel
Sprache:eng
Schlagworte:
Deformation analysis
Lie groups
Modules
Weight
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Zusammenfassung: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.
ISSN:2331-8422