2020/05/22 by Masaki Kashiwara, Myungho Kim, Kashiwara, Masaki +5
Mathematics · Physics and Astronomy · #17B37 #18D10 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2005.10969
openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Uq'(\mathfrakg) be a quantum affine algebra of untwisted affine ADE type, and C_\mathfrakg0 the Hernandez-Leclerc category of finite-dimensional Uq'(\mathfrakg)-modules. For a suitable infinite sequence \widehatw0= ⋯ s_i-1si0si1 ⋯ of simple reflections, we introduce subcategories C_\mathfrakg[a,b] of C_\mathfrakg0 for all a ≤ b ∈ ℤ\sqcup\ ± ∞ \. Associated with a certain chain \mathfrakC of intervals in [a,b], we construct a real simple commuting family M(\mathfrakC) in C_\mathfrakg[a,b], which consists of Kirillov-Reshetikhin modules. The category C_\mathfrakg[a,b] provides a monoidal categorification of the cluster algebra K(C_\mathfrakg[a,b]), whose set of initial cluster variables is [M(\mathfrakC)]. In particular, this result gives an affirmative answer to the monoidal categorification conjecture on C_\mathfrakg- by Hernandez-Leclerc since it is C_\mathfrakg[-∞,0], and is also applicable to C_\mathfrakg0 since it is C_\mathfrakg[-∞,∞].