Representations of the parafermion vertex operator algebras

2014/11/22 by Chongying Dong, Li Ren, Dong, Chongying +1 · 4 citations
Mathematics · Physics and Astronomy · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1411.6085

openalex publication_date 2014/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The rationality of the parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra and any nonnegative integer is established and the irreducible modules are determined.

Citations

• The commutant of L_\widehat\fraksl₂(n,0) in the vertex operator algebra L_\widehat\fraksl₂(1,0)^{⊗ n}
• Local systems of vertex operators, vertex superalgebras and modules
• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras

Cited by

• Rank-two parabolic-type VOAs and nilpotency of nil ideals
• Positivity of coinvariant divisors on M_0,n and the parafermions
• Quantum dimensions and fusion rules for parafermion vertex operator algebras
• Classification of irreducible highest weight modules for the parafermion vertex algebras N_k(\mathfraksl₂) at arbitrary level

Related

• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• The structure of parafermion vertex operator algebras: general case
• Automorphism groups of parafermion vertex operator algebras: general case
• Trace functions of the Parafermion vertex operator algebras
• Zhu's algebra, C₂-algebra and C₂-cofiniteness of parafermion vertex operator algebras