Irreducible representations of free products of matrix algebras

In this paper, we give a characterization of irreducible representation of ⁎i=1mMni(C) into MkN(C)MkN(C), where k∈Nk∈N and the least common multiple N   of n1,…,nmn1,…,nm is finite. We also give a necessary condition for the existence of irreducible representation of ⁎i=1mMni(C) into MkN(C)MkN(C).