Separability and a Lax Pair for the c_{2}{(1)} Toda lattice

Abstract

We consider the Toda lattice associated to the twisted affine Lie algebra 2 1 It is well known that this system is a two-dimensional algebraic completely integrable system By using algebraic geometric methods we give a linearisation of the system by determining the linearizing variables This allows us to explain a morphism between this system and the Mumford system Finally a Lax representation in terms of 2 x 2 matrices is constructed for this system