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