Representations of the Orbifold VOAS L(sl2)over-cap (k, 0)K and the Commutant VOAS CL(som)over-cap(1,0)⊗3(L(som)over-cap (3,0))

For the Klein group K, k is an element of Z(>= 1) and m is an element of Z(>= 4), we study the representations of the orbifold vertex operator algebra L-(sl2) over cap (k, 0)(K) and the commutant vertex operator algebra of L-(som) over cap(3, 0) in L-(som) over cap (1, 0)(circle times 3) which can be realized as the orbifold vertex operator subalgebra L-(sl2) over cap (2m, 0)(K) or its extension. All the irreducible modules for L-(sl2) over cap (k, 0)(K) and C-L (som) over cap ((1,0)circle times 3) (L-(som) over cap (3, 0)) are classified and constructed explicitly.