The 3-permutation orbifold of a lattice vertex operator algebra. (English) Zbl 1395.17067
The \(3\)-permution orbifold of rank one lattice vertex operator algebras are studied and the quantum dimensions and fusion rules of their irreducible modules are obtained. Additionally, the \(S\)-matrix is given and the irreducible modules are expressed in explicit forms. More generally, this paper is a continuation of a systematic study of permutation orbifolds of lattice vertex operator algebras by the authors. It follows the completion of the \(2\)-permutation case found in [Proc.Am.Math.Soc.144, No.8, 3207–3220 (2016; Zbl 1395.17065)] and [J.Algebra 476, 1–25 (2017; Zbl 1395.17066)]. While many of the techniques and proofs of the \(3\)-permutation case found in this work parallel the authors’ previous two papers, some new aspects are introduced (for example, the \(S\)-matrix calculation) and the analysis is more involved. Due to the authors’ use of known results for the orbifold vertex operator algebra \(V_{\sqrt{2}A_2}^\tau\) where \(\tau\) is an order \(3\) isometry of \(\sqrt{2}A_2\), only this particular \(3\)-orbifold is considered. The paper concludes with tables containing the explicit values of the \(19\times19\) \(S\)-matrix.
Reviewer: Matthew Krauel (Sacramento)
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
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