Fusion, mass, and representation theory of the Yangian algebra

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.