Abstract
We announce some results which involve some new, evidently integrable Toda type systems. More specifically, we construct a large family of Hamiltonian systems which interpolate between the classical Kostant-Toda lattice and the full Kostant-Toda lattice and we discuss their integrability. There is one such system for every nilpotent ideal I in a Borel subalgebra b+ of an arbitrary simple Lie algebra g. We mainly focus on the case when I is a height-2 ideal. Complete proofs of the announced results will appear in a future publication.
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