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