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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
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.

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Keywords: Plancherel's measure, tempered representation
Article copyright: © Copyright 1980 American Mathematical Society

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