Representations of the parafermion vertex operator algebras

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.

14 pages, major revision

References in corpus (3)

• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras
• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• The commutant of $L_{{\widehat{\mathfrak{sl}}}_2}(n,0)$ in the vertex operator algebra $L_{{\widehat{\mathfrak{sl}}}_2}(1,0{)}^{\otimes n}$

Cited by in corpus (6)

• Tensor categories for vertex operator superalgebra extensions
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• Modularity of logarithmic parafermion vertex algebras
• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• Representation theory of $L_k\left(\mathfrak{osp}(1|2)\right)$ from vertex tensor categories and Jacobi forms
• Quantum dimensions and fusion rules for parafermion vertex operator algebras