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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1999878
Page Count: 9
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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.
Transactions of the American Mathematical Society © 1980 American Mathematical Society