Extensions of tensor products of \(\mathbb{Z}_p\)-orbifold models of the lattice vertex operator algebra \(V_{\sqrt{2} A_{p - 1}}\). (English) Zbl 1457.17019
Summary: Let \(p\) be an odd prime and let \(\widehat{\sigma}\) be an order \(p\) automorphism of \(V_{\sqrt{2} A_{p - 1}}\) which is a lift of a \(p\)-cycle in the Weyl group \(\mathrm{Weyl}(A_{p - 1}) \cong \mathfrak{S}_p\). We study a certain extension \(V\) of a tensor product of finitely many copies of the orbifold model \(V_{\sqrt{2} A_{p - 1}}^{\langle \widehat{\sigma} \rangle}\) and give a criterion for \(V\) that every irreducible \(V\)-module is a simple current.
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 17B65 | Infinite-dimensional Lie (super)algebras |
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