Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 2 standard modules for D₄⁽¹⁾

2009/03/04 by Ivana Baranović, Baranović, Ivana
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras #math.QA

paper · pdf · doi:10.48550/arxiv.0903.0739

arxiv created 2009/03/04 · openalex publication_date 2009/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \gtl be an affine Lie algebra of type D_ℓ⁽¹⁾ and L(Λ) its standard module with a highest weight vector v_Λ. For a given \Z-gradation \gtl = \gtl_-1 + \gtl₀ + \gtl₁, we define Feigin-Stoyanovsky's type subspace as W(Λ) = U(\gtl₁) ⋅ v_Λ. By using vertex operator relations for standard modules we reduce the Ponicaré-Brikhoff-Witt spanning set of W(Λ) to a basis and prove its linear independence by using Dong-Lepowsky intertwining operators.

Citations

• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for \mathfrak sl(ℓ+1,\C)
• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard \gsl(ℓ+1,\C)-modules

Related

• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard \gsl(ℓ+1,\C)-modules
• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for \mathfrak sl(ℓ+1,\C)
• Bases of Feigin-Stoyanovsky's type subspaces for C_ℓ⁽¹⁾
• Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type C_ℓ⁽¹⁾
• Combinatorial bases of modules for affine Lie algebra B₂^(1)