On dominant ℓ--weights and maps between Weyl modules for quantum affine A_n

2025/04/27 by Matheus Brito, Vyjayanthi Chari, Brito, Matheus +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2504.19313

openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the set of dominant ℓ--weights in the Weyl (or standard) modules for quantum affine A_n. We then prove that the space of homomorphisms between standard modules is at most one-dimensional and give a necessary and sufficient condition for equality to hold. We also describe the socle of the standard module and prove that the socle is simple for large n. Finally, we give applications of our results to mixed Weyl modules, calculating extensions in the category and identify new families of tensor subcategories of finite dimensional representations.

Related

• Weyl Modules for Classical and Quantum Affine algebras
• Weight-finite modules over the quantum affine and double quantum affine algebras of type \mathfrak a₁
• Generalized Weyl modules and Demazure submodules of level-zero extremal weight modules
• Integrable and Weyl modules for quantum affine sl₂
• Weight modules of quantized Weyl algebras