Principal subspaces of higher-level standard \widehat\mathfraksl(n)-modules

2014/05/31 by Christopher Sadowski, Sadowski, Christopher
Mathematics · #17B65 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B65 #msc:17B69

paper · pdf · doi:10.48550/arxiv.1406.0095

35 pages

arxiv created 2014/05/31 · openalex publication_date 2014/05/31 · arxiv updated 2014/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex operator algebras and intertwining operators to construct exact sequences among principal subspaces of certain standard \widehat\mathfraksl(n)-modules, n ≥ 3. As a consequence, we obtain the multigraded dimensions of the principal subspaces W(k₁Λ₁ + k₂ Λ₂) and W(k_n-2Λ_n-2 + k_n-1 Λ_n-1). This generalizes earlier work by Calinescu on principal subspaces of standard \widehat\mathfraksl(3)-modules.

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