Abstract

Lebesgue measure on the linear dual of the Lie algebra of an exponential solvable Lie group is decomposed into semi-invariant orbital measures by means of a detailed analysis of orbital parameters and a natural measure on an explicit cross-section for generic coadjoint orbits. This decomposition yields a precise and explicit description of the Plancherel measure.

Keywords

coadjoint orbit, representation, polarization

Mathematical Subject Classification

Primary: 22E25, 22E27

Authors