Delius G.W., Gould M.D., Zhang Y.-Z.
On the Construction of Trigonometric Solutions of the Yang-Baxter Equation
(80K, LATEX)

ABSTRACT.  We describe the construction of trigonometric R-matrices corresponding to 
the (multiplicity-free) tensor product of any two irreducible representations 
of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor
product graph method to the case of two different representations.
It yields the decomposition of the R-matrix
into projection operators. Many new examples of trigonometric R-matrices 
(solutions to the spectral parameter dependent Yang-Baxter equation) are
constructed using this approach.