Weyl Modules for Classical and Quantum Affine algebras

2000/04/27 by Vyjayanthi Chari, Chari, Vyjayanthi, Andrew Pressley +1 · 5 citations
Mathematics · #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0004174

arxiv created 2000/04/27 · openalex publication_date 2000/04/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the quantum affine algebras. We prove this conjecture in the case of affine sl₂. We establish a criterion for these modules to be irreducible and prove a factorization theorem for them in the general case.

Cited by

• Weyl modules for equivariant map Lie superalgebras
• Tensor products of level zero representations
• Positive level, negative level and level zero
• Integrable and Weyl modules for quantum affine sl₂
• Graded representations of current Lie superalgebras \mathfraksl(1|2)[t]

Related

• Integrable and Weyl modules for quantum affine sl₂
• On dominant ℓ--weights and maps between Weyl modules for quantum affine A_n
• Quantum Affine Algebras and their Representations
• Demazure modules of level two and prime representations of quantum affine \mathfraksl_n+1
• Irreducible Modules for the Quantum Affine Algebra U_q(g) and its Borel subalgebra U_q(g)^{≥ 0}