THE ANALYTIC STRUCTURE OF TRIGONOMETRIC S-MATRICES

S-matrices associated to the vector representations of the quantum gro ups for the classical Lie algebras are constructed. For the a(m-1) and c(m) algebras the complete S-matrix is found by an application of the bootstrap equations. It is shown that the simplest form for the S-mat rix which generalizes that of the Gross-Neveu model is not consistent for the non-simply-laced algebras due to the existence of unexplained singularities on the physical strip. However, a form which generalizes the S-matrix of the principal chiral model is shown to be consistent via an argument which uses a novel application of the Coleman-Thun mec hanism. The analysis also gives a correct description of the analytic structure of the S-matrix of the principle chiral model for c(m).