This paper uses
momentum mappings on generalized flag manifolds and their momentum
polytopes to study the geometry of the level sets of the 1-chop integrals
of the full Kostant-Toda lattice in certain isospectral submanifolds of the
phase space. Expressions for these integrals are derived in terms of Plücker
coordinates on the flag manifold in the case that all eigenvalues are zero, and the
geometry of the base locus of their level set varieties is compared with the
corresponding geometry for distinct eigenvalues. These results are illustrated
and extended in the context of the full sl(3,C) and sl(4,C) Kostant-Toda
lattices.
