2009/09/06 by Jae-Hoon Kwon, Kwon, Jae-Hoon
Mathematics · Physics and Astronomy · #05E10 #17B37 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:05E10 #msc:17B37
paper · pdf · doi:10.48550/arxiv.0909.1126
openalex publication_date 2009/09/06 · arxiv created 2011/01/11 · arxiv updated 2011/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a category of \gl_∞-crystals, whose objects are disjoint unions of extremal weight crystals of non-negative level with certain finite conditions on the multiplicity of connected components. We show that it is a monoidal category under tensor product of crystals and the associated Grothendieck ring is anti-isomorphic to an Ore extension of the character ring of integrable lowest weight \gl_∞-modules with respect to derivations shifting the characters of fundamental modules. A Littlewood-Richardson rule of extremal weight crystals with non-negative level is described explicitly in terms of classical Littlewood-Richardson coefficients.