Canonical coordinates for coadjoint orbits of completely solvable groups.
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...