Verma-type Modules for Quantum Affine Lie Algebras

2000/10/31 by Vyacheslav Futorny, Vyacheslav M. Futorny, Duncan J. Melville +5
Mathematics · Physics and Astronomy · #17B37 #17B67 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:17B67 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0010322

24 pages, AMSTeX 2.0

arxiv created 2000/10/31 · openalex publication_date 2000/10/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(ł) in the sense that the weight structure is preserved under the deformation. We also analyze the submodule structure of quantum Verma-type modules.

Related

• Kashiwara Algebras and Imaginary Verma Modules for U_q(\mathfrakg)
• Representations of Affine Quantum Function Algebras
• Extremal weight modules of quantum affine algebras
• Imaginary Verma modules and Kashiwara algebras for U_q(\widehat\mathfraksl(2))
• Colored Kac-Moody Algebras, Part I