2010/03/29 by Bin Li, Li, Bin, Hechun Zhang +1
Mathematics · Physics and Astronomy · #17B37 #20G42 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:20G42 #msc:81R50
paper · pdf · doi:10.48550/arxiv.1003.5416
19pages, 1 figure
arxiv created 2010/03/29 · openalex publication_date 2010/03/29 · arxiv updated 2010/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a quantized enveloping algebra Uq(\mathfrak g) and a pair of dominant weights (λ, μ), we extend a conjecture raised by Lusztig in \citeLusztig:1992to a more general form and then prove this extended Lusztig's conjecture. Namely we prove that for any symmetrizable Kac-Moody algebra \mathfrak g, there is a composition series of the Uq(\mathfrak g)-module V(λ)⊗ V(μ) compatible with the canonical basis. As a byproduct, the celebrated Littlewood-Richardson rule is derived and we also construct, in the same manner, a composition series of V(λ)⊗ V(-μ) compatible with the canonical basis when \mathfrak g is of affine type and the level of λ-μ is nonzero.