The flow of the G(2) periodic Toda lattice

In the study of the generalized periodic Toda lattices, Mark Adler and Pierre van Moerbeke showed that the flow of the G(2) periodic Toda lattice has a 2-dimensional sub-Abelian variety of a 3-dimensional Prym variety as its Hamiltonian torus. In this paper it is shown that the 2-dimensional torus is a Prym-Tjurin variety and is explained in terms of the Weyl group of G(2). This example is small enough to be explicitly computable. (C) 1997 American Institute of Physics.