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Transactions of the American Mathematical Society

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On Harish-Chandra's $ \mu $-function for $ p$-adic groups


Author: Allan J. Silberger
Journal: Trans. Amer. Math. Soc. 260 (1980), 113-121
MSC: Primary 22E50
DOI: https://doi.org/10.1090/S0002-9947-1980-0570781-7
MathSciNet review: 570781
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Abstract: The Harish-Chandra $ \mu $-function is, up to known constant factors, the Plancherel's measure associated to an induced series of representations. In this paper we show that, when the series is induced from special representations lifted to a parabolic subgroup, the $ \mu $-function is a quotient of translated $ \mu $-functions associated to series induced from supercuspidal representations. It is now known, in both the real and p-adic cases, that the $ \mu $-function is always an Euler factor.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0570781-7
Keywords: Plancherel's measure, tempered representation
Article copyright: © Copyright 1980 American Mathematical Society

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