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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A Plancherel formula for parabolic subgroups


Author: Mie Nakata
Journal: Trans. Amer. Math. Soc. 319 (1990), 243-256
MSC: Primary 22E35; Secondary 22E50, 43A32
MathSciNet review: 1019522
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Abstract: We obtain explicit Plancherel formulas for the parabolic subgroups $ P$ of $ p$-adic unitary groups which fix one dimensional isotropic subspaces. By means of certain limits of difference operators (called strong derivatives), we construct a Dixmier-Pukanszky operator which compensates for the nonunimodularity of the group $ P$.

Then, we compute the Plancherel formula of $ N \cdot A$, where $ N$ is the nilradical of $ P$ and $ A = {Q'_p}$, the multiplicative group of nonzero $ p$-adic numbers, by formulating a $ p$-adic change of variable formula and using the strong derivative.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1019522-6
PII: S 0002-9947(1990)1019522-6
Keywords: Parabolic subgroup, $ p$-adic number field, Plancherel formula, Dixmier-Pukanszky operator, strong derivative
Article copyright: © Copyright 1990 American Mathematical Society