Characters of the Nullcone.
All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.
We introduce a new class of connected solvable Lie groups called -group. Namely a -group is a unimodular connected solvable Lie group with center such that for some in the Lie algebra of , the symplectic for on given by is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group with center , such that the center of is finite, has discrete series if and only if may be written as , , where is a -group with...