Extensions of tensor products of ${\mathbb Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1}}$

Abstract: 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 ${\rm Weyl}(A_{p-1})\cong {\mathfrak S}p$. 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.