Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type C_ℓ⁽¹⁾

2017/09/15 by Trupčević, Goran
#05A19(Secondary) #17B67 (Primary) #17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1709.05121

Abstract

Feigin-Stoyanovsky's type subspace W(Λ) of a standard \mathfrak g-module L(Λ) is a \mathfrak g₁-submodule of L(Λ) generated by the highest-weight vector v_Λ, where \mathfrak g₁ is a certain commutative subalgebra of \mathfrak g. Based on the description of basis of W(Λ) for \mathfrak g of type C_ℓ⁽¹⁾, we give a presentation of this subspace in terms of generators and relations W(Λ)≃ U(\mathfrak g₁^-)/J.

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