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It is known that the unitary representation of the D=4, N=4 superconformalmultiplets and their descendants are constructed as supercoherent states ofbosonic and fermionic creation oscillators which covariantly transform underSU(2,2|4). We non-linearly realize those creation oscillators on the cosetsuperspace PSU(2,2|4)/{SO(1,4) x SO(5)} which is reparametrized by the D=10supercoordinates. We consider a D=2 non-linear sigma model on the cosetsuperspace and set up Poisson brackets for the D=10 supercoordinates on thelight-like line. It is then shown that the non-linearly realized creationoscillators satisfy the classical exchange algebra with the classical r-matrixof PSU(2,2|4). We have recourse to purely algebraic quantization of theclassical exchange algebra in which the r-matrix is promoted to the universalR-matrix. The quantum exchange algebra essentially characterizes correlationfunctions of the D=4, N=4 superconformal multiplets and their descendants onthe light-like line. The arguments are straightforwardly extended to the casewhere those quantities are endowed with the U(N) YM gauge symmetry.

PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets