A Plancherel formula for idyllic nilpotent Lie groups
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- by Eloise Carlton PDF
- Trans. Amer. Math. Soc. 224 (1976), 1-42 Request permission
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 ${A_l},{C_l},{G_2}$. 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 Plancherel measures of ${G_\gamma }/N$, where ${G_\gamma }$ is the stability subgroup at $\gamma$ in N. When both N and ${G_\gamma }/N$ are abelian, the measures (1) and (2) are obtained as special cases of more general problems. These measures combine into Plancherel measure for G.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 224 (1976), 1-42
- MSC: Primary 22E25
- DOI: https://doi.org/10.1090/S0002-9947-1976-0425014-8
- MathSciNet review: 0425014