Explicit orbital parameters and the Plancherel measure for exponential Lie groups

Bradley N. Currey

Vol. 219 (2005), No. 1, 97–138

DOI: 10.2140/pjm.2005.219.97

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 2000

Primary: 22E25, 22E27

Milestones

Received: 1 April 2003

Revised: 12 May 2004

Published: 1 March 2005