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.