A path description for ε-characters of representations of type A restricted quantum loop algebras at roots of unity

2025/03/07 by An, Xiao-Juan, Li, Jian-Rong, Luo, Yan-Feng +1
#17B37 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2503.05440

Abstract

Fix ε^2ℓ=1 with ℓ ≥ 2. In this paper, we show that all finite-dimensional simple modules of any restricted quantum loop algebra U_ε^{\rm res}(L\mathfraksl_n+1) in a certain category can be transformed into snake modules. We obtain an effective and concrete path description for ε-characters of any simple module with highest l-weight of degree two and any Kirillov-Reshetikhin module of U_ε^{\rm res}(L\mathfraksl_n+1). As an application of our path description, we obtain a necessary and sufficient condition for the tensor product of two fundamental representations of U_ε^{\rm res}(L\mathfraksl_n+1) to be irreducible. Additionally, we obtain a necessary condition for the tensor product of two or more fundamental representations of U_ε^{\rm res}(L\mathfraksl_n+1) to be irreducible.

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