Spectrum and multiplicities for restrictions of unitary representations in nilpotent Lie groups

Lawrence Jay Corwin and Frederick Paul Greenleaf

Vol. 135 (1988), No. 2, 233–267

DOI: 10.2140/pjm.1988.135.233

Abstract

Let G be a connected, simply connected nilpotent Lie group, and let AT be a Lie subgroup. We consider the following question: for n < G G^A, how does one decompose U∖K as a direct integral? In his pioneering paper on representations of nilpotent Lie groups, Kirillov gave a qualitative description; our answer here gives the multiplicities of the representations appearing in the direct integral, but is geometric in nature and very much in the spirit of the Kirillov orbit picture.

Mathematical Subject Classification 2000

Primary: 22E27

Milestones

Received: 8 June 1987

Published: 1 December 1988