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On Harish-Chandra's μ-Function for p-Adic Groups

Allan J. Silberger
Transactions of the American Mathematical Society
Vol. 260, No. 1 (Jul., 1980), pp. 113-121
DOI: 10.2307/1999878
Stable URL: http://www.jstor.org/stable/1999878
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Harish-Chandra's μ-Function for p-Adic Groups
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Abstract

The Harish-Chandra μ-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 μ-function is a quotient of translated μ-functions associated to series induced from supercuspidal representations. It is now known, in both the real and p-adic cases, that the μ-function is always an Euler factor.

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