ABSTRACT. A procedure is developed which can be used to compute the Plancherel measure for a certain class of nilpotent Lie groups, including the Heisenberg groups, free groups, two-and three-step groups, the nilpotent part of an Iwasawa decomposition of the R-split form of the classical simple groups A,, C¡, G2.Let G be a connected, simply connected nilpotent Lie group. The Plancherel formula for G can be expressed in terms of Plancherel measure of a normal subgroup N and projective Plancherel measures of certain subgroups of G ¡N. To get an explicit measure for G, we need an explicit formula for (1) the disintegration of Plancherel measure of N under the action of G on N, and (2) projective A
ELOISE CARLTON projective measures are reasonable. The method works for those connected, simply connected, nilpotent Lie groups G which have an abelian normal Lie subgroup A N such that for pN almost all y E N, Gy/N is abelian, where Gy is the stability subgroup at y for the action of G on N. Such a nilpotent Lie group is called
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