A Gentle (without Chopping) Approach to the Full Kostant-Toda Lattice

Abstract

In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space of maps from Z_n to GL(n,R) endowed with a structure of a pair of Lie-algebroids.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA