Pantelis DAMIANOU and FRANCO MAGRI
Department of Mathematics and Statistics,
University of Cyprus,
P. O. Box 20537,
1678 Nicosia,
CYPRUS
     and
Department of Mathematics,
University of Milano,
Bicocca, Via degli Arcimboldi 8,
Edificio V7,
20126 Milano,
ITALY
E-mail: damianou@ucy.ac.cy, magri@matapp.unimib.it

A gentle (without chopping) approach to the Full-Kostant-Toda Lattice

Abstract:
We propose a new algorithm for obtaining the rational invariants for the Full-Kostant-Toda lattice. It is well-known that the KdV is obtained by reducing the space of maps from $S^1$ to $gl(2, R)$. A discrete version of this approach replaces $S^1$ by $Z_n$ and the target space by $GL(n,R)$. A further reduction of these
new discrete integrable hierarchies produces the Full-Kostant-Toda lattice.