Commutant of L_\widehat\mathfraksl₂(4,0) in the cyclic permutation orbifold of L_\widehat\mathfraksl₂(1,0)^{⊗ 4}

2014/04/08 by Toshiyuki Abe, Abe, Toshiyuki, Hiromichi Yamada +1
Mathematics · Physics and Astronomy · #17B69 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B69

paper · pdf · doi:10.48550/arxiv.1404.1974

13 pages, no figure

arxiv created 2014/04/08 · openalex publication_date 2014/04/08 · arxiv updated 2014/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the commutant of the vertex operator algebra L_\widehat\mathfraksl₂(4,0) in the cyclic permutation orbifold model (L_\widehat\mathfraksl₂(1,0)^{⊗ 4})^τ with τ=(1 2 3 4). It is shown that the commutant is isomorphic to a \mathbb Z₂×\mathbb Z₂-orbifold model of a tensor product of two lattice type vertex operator algebras of rank one.

Citations

• The commutant of L_\widehat\fraksl₂(n,0) in the vertex operator algebra L_\widehat\fraksl₂(1,0)^{⊗ n}

Related

• The commutant of L_\widehat\fraksl₂(n,0) in the vertex operator algebra L_\widehat\fraksl₂(1,0)^{⊗ n}
• Representations and fusion rules for the orbifold vertex operator algebras L_\widehat\fraksl₂(k,0)^ℤ₃
• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras
• Cyclic permutations of lattice vertex operator algebras
• S-matrix in permutation orbifolds