Let A" be a Lie subgroup of the connected, simply connected nilpotent Lie group G, and let f, g be the corresponding Lie algebras. Suppose that a is an irreducible unitary representation of K. We give an explicit direct integral decomposition of IndA^c;o into irreducibles. The description uses the Kirillov orbit picture, which gives a bijection between GA and the coadjoint orbits in g* (and sim...
