N=4 Multiplets in N=3 Harmonic Superspace

It is shown that the N=3 harmonic-superfield equations of motion are invariant with respect to the 4-th supersymmetry. The SU(3) harmonics are also used to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An alternative unusual representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. U(1) charges of superfields in these multiplets are parametrized by an integer- valued parameter which plays the role of the discrete coordinate. Each superfield term of the N=3 Yang-Mills action has the infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters.