  Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to
analyze the structure of tensor products of the Yangian algebra representations
is presented. We then apply the results to the $S$-matrix theory of the
$G\otimes G$-invariant nonlinear $\sigma$-model ($G$-principal chiral model) by
Ogievetsky, Reshetikhin, and Wiegmann. We show how the physical data such as
mass formula, fusion angle, and the spins of integrals of motion can be
extracted from the Yangian highest weight representations.
