Representations of ${\mathbb{Z}}_2$-orbifold of the parafermion vertex operator algebra $K(s{l}_2,k)$

In this paper, the irreducible modules for the ${\mathbb{Z}}_2$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ of level $k$ are classified and constructed.