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

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.