Bimodules associated to modules of vertex operator algebras

Abstract

Let V be a vertex operator algebra, M be an admissible V-module. An $A_n(V)$-$A_m(V)$-bimodule $A_{n,m}(M)$ for any nonnegative integers m and n is constructed and studied. The fusion rules for admissible V-modules are determined in terms of bimodule $A_{n,m}(M)$. $A_{n,m}(M)$ for irreducible V-module M is given explicitly if V is rational.

Keywords:

• Bimodule
• Lie algebra
• representation
• vertex algebra
• vertex operator algebra

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B69

Additional information

Funding

Wei Jiang is supported by China NSF grants (11671056, 11701047), the NSF of Jiangsu (BK20160403) and the NSF of Zhejiang (LQ12A01005). Wei Zhang, supported in part by the China NSF (11101030), Beijing Higher Education Young Elite Teacher Project and Morningside Center of Mathematics.