2008/07/22 by Goran Trupčević, Trupčević, Goran · 1 citation
Mathematics · #05A19 (Secondary) #17B67 (Primary) 17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.QA #math.RT #msc:05A19 #msc:17B67 #msc:17B69
paper · pdf · doi:10.48550/arxiv.0807.3363
22 pages, 7 figures, AMS-LaTeX
arxiv created 2008/07/22 · openalex publication_date 2008/07/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let \mathfrak g be an affine Lie algebra of type A_ℓ(1). Suppose we're given a \mathbb Z-gradation of the corresponding simple finite-dimensional Lie algebra \mathfrak g=\mathfrak g-1⊕\mathfrak g0 ⊕ \mathfrak g1; then we also have the induced \mathbb Z-gradation of the affine Lie algebra \mathfrak g=\mathfrak g-1 ⊕ \mathfrak g0 ⊕ \mathfrak g1. Let L(Λ) be a standard module of level 1. Feigin-Stoyanovsky's type subspace W(Λ) is the \mathfrak g1-submodule of L(Λ) generated by the highest-weight vector vΛ, W(Λ)=U(\mathfrak g1)⋅ vΛ⊂ L(Λ). We find a combinatorial basis of W(Λ) given in terms of difference and initial conditions. Linear independence of the generating set is proved inductively by using coefficients of intertwining operators. A basis of L(Λ) is obtained as an ``inductive limit'' of the basis of W(Λ).