A uniform trigonometric R-matrix for the exceptional series

We give a uniform trigonometric R-matrix for the adjoint representations on the exceptional series. The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. For L a simple Lie algebra there is a rational R-matrix in EndL(⊗²(L⊕ I)) which has a quantum deformation to a trigonometric R-matrix. We construct a sixteen dimensional algebra, A⁽2), which interpolates the quantum deformations of the algebras EndL(⊗²(L⊕ I)) and a 287 dimensional algebra, A⁽3), which interpolates the quantum deformations of the algebras EndL(⊗³(L⊕ I)). Then we construct an R-matrix in A⁽2) which satisfies the Yang--Baxter equation in A⁽3) and which interpolates the trigonometric R-matrices for the points in the exceptional series.