ROOT SYSTEMS AND PURELY ELASTIC S-MATRICES

A "fusing rule" for the three-point couplings in the known purely elastic scattering theories is proposed, in terms of which various universal features of these models have a simple explanation. A hypothesised expression for the general S-matrix element is shown to satisfy the bootstrap relations following from these couplings, and used to relate each S-matrix to the matrix of a particular Coxeter element in the relevant basis of simple roots.