Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 2 Standard Modules for

Abstract

Let be an affine Lie algebra of type and L(Λ) its standard module with a highest weight vector v _Λ. For a given ℤ-gradation , we define Feigin–Stoyanovsky's type subspace as

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.

Key Words:

• Affine Lie algebra
• Combinatorial basis
• Feigin–Stoyanovsky's subspace
• Intertwining operators
• Principal subspace
• Simple current operator
• Standard modules
• Vertex algebra

2000 Mathematics Subject Classification:

• Primary 17B67
• Secondary 17B69, 05A19

ACKNOWLEDGMENT

Partially supported by the Ministry of Science and Technology of the Republic of Croatia, Project ID 037-0372794-2806. I thank Mirko Primc for his help on the topic and valuable suggestions.

I thank Mirko Primc for his help on the topic and valuable suggestions.

Notes

Communicated by K. Misra.