Coadjoint orbits of stepwise square integrable representations (Q2790210)

The paper under review provides an alternative approach to the study of stepwise square integrable representations of nilpotent Lie groups using the method of coadjoint orbits. This approach relates the study to the stratifications of duals of nilpotent Lie algebras and thus leads directly to basic properties of stepwise square integrable representations such as the fact that they correspond to a subset with relative Hausdorff topology, dense interior, and total Plancherel measure in the unitary dual of the Lie group under consideration. In the special case of strictly upper triangular groups, one obtains the principal series representations of Dixmier.