Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 1 Standard Modules for

Abstract

Let be an affine Lie algebra of the type . Suppose we are given a ℤ-gradation of the corresponding simple finite-dimensional Lie algebra 𝔤 = 𝔤₋₁ ⊕ 𝔤₀ ⊕ 𝔤₁; then we also have the induced ℤ-gradation of the affine Lie algebra

Let L(Λ) be a standard module of level 1. Feigin–Stoyanovsky's type subspace W(Λ) is the -submodule of L(Λ) generated by the highest-weight vector v _Λ,

We find a combinatorial basis of W(Λ) given in terms of difference and initial conditions.

Key Words:

• Affine Lie algebras
• Combinatorial bases
• Standard modules
• Vertex operator algebras

2000 Mathematics Subject Classification:

• Primary 17B67
• Secondary 17B69, 05A19

ACKNOWLEDGMENTS

Partially supported by the Ministry of Science and Technology of the Republic of Croatia, Project ID 037-0372794-2806.

Notes

Communicated by K. Misra.