2024/12/30 by Hyeonjae Choi, Choi, Hyeonjae, Donghyun Kim +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.20757
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lusztig q-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of Kirillov-Reshetikhin crystals. Specifically, for type C with dominant weights and type B with dominant spin weights, we present a combinatorial formula for Lusztig q-weight multiplicities in terms of energy functions of Kirillov-Reshetikhin crystals, generalizing the charge statistic on semistandard Young tableaux for type A. Additionally, we introduce level-restricted q-weight multiplicities for nonexceptional types, and prove positivity by providing their combinatorial formulas.