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In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifoldvertex operator subalgebra of the parafermion vertex operator algebraassociated to the irreducible highest weight modules for the affine Kac-Moodyalgebra $A_1^{(1)}$ of level $k$ are classified and constructed.

Representations of $\mathbb{Z}_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$